## Jeyakumar, Vaithilingam

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 Author ID: jeyakumar.vaithilingam Published as: Jeyakumar, V.; Jeyakumar, Vaithilingam Homepage: https://research.unsw.edu.au/people/professor-jeya-jeyakumar External Links: MGP · ORCID · Google Scholar · dblp
 Documents Indexed: 177 Publications since 1984, including 1 Book 1 Contribution as Editor Co-Authors: 51 Co-Authors with 151 Joint Publications 1,601 Co-Co-Authors
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### Co-Authors

 21 single-authored 54 Li, Guoyin 22 Lee, Gue Myung 13 Chuong, Thai Doan 10 Wu, Zhiyou 9 Dinh The Luc 9 Goberna, Miguel Angel 9 Rubinov, Alexander M. 9 Srisatkunarajah, Sivakolundu 7 Huy, Nguyen Quang 6 Vicente-Pérez, José 6 Yang, Xiaoqi 5 Gwinner, Joachim 4 Burachik, Regina Sandra 4 Chieu, Nguyen Huy 4 Mohebi, Hossein 4 Oettli, Werner 3 Craven, Bruce Desmond 3 Wang, Jinhua 3 Woolnough, Daniel 2 Ishizuka, Yo 2 Lasserre, Jean-Bernard 2 Lee, Jae Hyoung 2 López-Cerdá, Marco Antonio 2 Phạm Tiên So’n 2 Wang, Xiang 2 Wolkowicz, Henry 1 Bomze, Immanuel M. 1 Boţ, Radu Ioan 1 Brew, Bruce J. 1 Cysique, Lucette A. 1 Demyanov, Vladimir Fedorovich 1 Dunbar, Michelle 1 Jeyakumar, Niroshan 1 Loy, Clement T. 1 Mond, Bertram 1 Mordukhovich, Boris S. 1 Murray, John M. 1 Natividad, Maria Caridad 1 Nealon, Michael J. 1 Ormerod, John T. 1 Schaible, Siegfried 1 Srisatkunrajah, S. 1 Studniarski, Marcin 1 Suthaharan, Shan 1 Théra, Michel A. 1 Tinh, Phan Nhat 1 Tuan, Hoang Duong 1 Vũ Ngoc Phát 1 Weir, Terence 1 Nguyen Dong Yen 1 Zaffaroni, Alberto
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### Serials

 26 Journal of Optimization Theory and Applications 14 Journal of Global Optimization 12 Mathematical Programming. Series A. Series B 12 SIAM Journal on Optimization 10 Operations Research Letters 10 Optimization 10 European Journal of Operational Research 9 Journal of Convex Analysis 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Journal of Mathematical Analysis and Applications 6 Optimization Letters 4 Pacific Journal of Optimization 4 Nonlinear Analysis. Theory, Methods & Applications 3 Numerical Functional Analysis and Optimization 3 Linear Algebra and its Applications 2 Bulletin of the Australian Mathematical Society 2 Journal of the Australian Mathematical Society, Series B 2 Journal of Approximation Theory 2 Utilitas Mathematica 2 Applied Mathematics Letters 2 Set-Valued Analysis 2 Top 1 Applicable Analysis 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Applied Mathematics and Computation 1 Mathematics of Operations Research 1 Opsearch 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Control and Optimization 1 Asia-Pacific Journal of Operational Research 1 Journal of the Australian Mathematical Society. Series A 1 Zeitschrift für Operations Research. Serie A: Theorie 1 ZOR. Zeitschrift für Operations Research 1 Optimization Methods & Software 1 Positivity 1 Optimization and Engineering 1 RAIRO. Operations Research 1 Journal of Nonlinear and Convex Analysis 1 The ANZIAM Journal 1 Methods of Operations Research 1 Applied Optimization 1 Set-Valued and Variational Analysis 1 Springer Optimization and Its Applications
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### Fields

 163 Operations research, mathematical programming (90-XX) 66 Calculus of variations and optimal control; optimization (49-XX) 13 Numerical analysis (65-XX) 12 Approximations and expansions (41-XX) 11 Real functions (26-XX) 7 Functional analysis (46-XX) 6 Operator theory (47-XX) 5 Convex and discrete geometry (52-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Algebraic geometry (14-XX) 3 Computer science (68-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Statistics (62-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

167 Publications have been cited 2,934 times in 1,329 Documents Cited by Year
On generalised convex mathematical programming. Zbl 0773.90061
Jeyakumar, V.; Mond, B.
1992
Approximate Jacobian matrices for nonsmooth continuous maps and $$C^{1}$$-optimization. Zbl 0923.49012
Jeyakumar, V.; Luc, D. T.
1998
Nonsmooth calculus, minimality, and monotonicity of convexificators. Zbl 0956.90033
Jeyakumar, V.; Luc, D. T.
1999
New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs. Zbl 1046.90059
Jeyakumar, V.; Lee, G. M.; Dinh, N.
2003
Strong duality in robust convex programming: complete characterizations. Zbl 1228.90075
Jeyakumar, V.; Li, G. Y.
2010
A class of nonconvex functions and mathematical programming. Zbl 0639.90082
Weir, T.; Jeyakumar, V.
1988
Strong and weak invexity in mathematical programming. Zbl 0566.90086
Jeyakumar, V.
1985
A solvability theorem for a class of quasiconvex mappings with applications to optimization. Zbl 0791.46002
Jeyakumar, V.; Oettli, W.; Natividad, M.
1993
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions. Zbl 1206.90178
Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
2007
Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization. Zbl 1297.90105
Jeyakumar, V.; Li, G. Y.
2014
Convexlike alternative theorems and mathematical programming. Zbl 0581.90079
Jeyakumar, V.
1985
Generalizations of Slater’s constraint qualification for infinite convex programs. Zbl 0771.90078
Jeyakumar, V.; Wolkowicz, Henry
1992
Nonsmooth vector functions and continuous optimization. Zbl 1138.90002
Jeyakumar, V.; Dinh The Luc
2008
Characterizing set containments involving infinite convex constraints and reverse-convex constraints. Zbl 1038.90061
Jeyakumar, V.
2003
Hunting for a smaller convex subdifferential. Zbl 0872.90083
Demyanov, V. F.; Jeyakumar, V.
1997
A new geometric condition for Fenchel’s duality in infinite dimensional spaces. Zbl 1093.90077
Burachik, Regina Sandra; Jeyakumar, Vaithilingam
2005
A dual condition for the convex subdifferential sum formula with applications. Zbl 1098.49017
Burachik, R. S.; Jeyakumar, V.
2005
Convex composite multi-objective nonsmooth programming. Zbl 0789.90068
Jeyakumar, V.; Yang, X. Q.
1993
On characterizing the solution sets of pseudolinear programs. Zbl 0840.90118
Jeyakumar, V.; Yang, X. Q.
1995
Robust solutions to multi-objective linear programs with uncertain data. Zbl 1341.90124
Goberna, M. A.; Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2015
Alternative theorems for quadratic inequality systems and global quadratic optimization. Zbl 1197.90315
Jeyakumar, V.; Lee, G. M.; Li, G. Y.
2009
A generalization of a minimax theorem of Fan via a theorem of the alternative. Zbl 0563.49006
Jeyakumar, V.
1986
Zero duality gaps in infinite-dimensional programming. Zbl 0687.90077
Jeyakumar, V.; Wolkowicz, H.
1990
Generalized second-order directional derivatives and optimization with $$C^{1,1}$$ functions. Zbl 0814.49012
Yang, X. Q.; Jeyakumar, V.
1992
Characterizations of solution sets of convex vector minimization problems. Zbl 1103.90090
Jeyakumar, V.; Lee, G. M.; Dinh, N.
2006
Necessary and sufficient constraint qualifications for solvability of systems of infinite convex inequalities. Zbl 1145.90051
Goberna, M. A.; Jeyakumar, V.; López, M. A.
2008
Sufficient global optimality conditions for non-convex quadratic minimization problems with box constraints. Zbl 1131.90060
Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
2006
Constraint qualifications characterizing Lagrangian duality in convex optimization. Zbl 1194.90069
Jeyakumar, V.
2008
Inequality systems and global optimization. Zbl 0856.90128
Jeyakumar, V.; Rubinov, A. M.; Glover, B. M.; Ishizuka, Y.
1996
Characterizing robust set containments and solutions of uncertain linear programs without qualifications. Zbl 1220.90067
Jeyakumar, V.; Li, Guoyin
2010
Robust conjugate duality for convex optimization under uncertainty with application to data classification. Zbl 1233.90231
Li, G. Y.; Jeyakumar, V.; Lee, G. M.
2011
Lagrange multiplier conditions characterizing the optimal solution sets of cone-constrained convex programs. Zbl 1114.90091
Jeyakumar, V.; Lee, G. M.; Dinh, N.
2004
Robust solutions of multiobjective linear semi-infinite programs under constraint data uncertainty. Zbl 1325.90081
Goberna, M. A.; Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2014
Asymptotic dual conditions characterizing optimality for infinite convex programs. Zbl 0901.90158
Jeyakumar, V.
1997
Composite nonsmooth programming with Gâteaux differentiability. Zbl 0752.90067
Jeyakumar, V.
1991
Equivalence of saddle-points and optima, and duality for a class of non- smooth non-convex problems. Zbl 0642.49018
Jeyakumar, V.
1988
Complete characterizations of stable Farkas’ lemma and cone-convex programming duality. Zbl 1145.90074
Jeyakumar, V.; Lee, G. M.
2008
The strong conical hull intersection property for convex programming. Zbl 1134.90462
Jeyakumar, V.
2006
Inequality systems and optimization. Zbl 0734.90089
Jeyakumar, V.; Gwinner, J.
1991
Robust linear semi-infinite programming duality under uncertainty. Zbl 1282.90204
Goberna, M. A.; Jeyakumar, V.; Li, G.; López, M. A.
2013
Necessary and sufficient conditions for stable conjugate duality. Zbl 1091.49031
Burachik, R. S.; Jeyakumar, V.; Wu, Z.-Y.
2006
A sharp Lagrange multiplier rule for nonsmooth mathematical programming problems involving equality constraints. Zbl 1047.90075
Wang, Xiang; Jeyakumar, V.
2000
Robust duality in parametric convex optimization. Zbl 1327.90195
Boţ, R. I.; Jeyakumar, V.; Li, G. Y.
2013
Characterizing robust solution sets of convex programs under data uncertainty. Zbl 1307.90136
Jeyakumar, V.; Lee, G. M.; Li, G.
2015
A simple closure condition for the normal cone intersection formula. Zbl 1065.46055
Burachik, Regina Sandra; Jeyakumar, Vaithilingam
2005
On optimality conditions in nonsmooth inequality constrained minimization. Zbl 0611.90081
Jeyakumar, V.
1987
Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with $$C^1$$-data. Zbl 0954.90053
Jeyakumar, V.; Wang, X.
1999
Robust duality for generalized convex programming problems under data uncertainty. Zbl 1254.90154
Jeyakumar, V.; Li, G.; Lee, G. M.
2012
Robust SOS-convex polynomial optimization problems: exact SDP relaxations. Zbl 1338.90452
Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2015
Necessary and sufficient conditions for $$S$$-lemma and nonconvex quadratic optimization. Zbl 1273.90141
Jeyakumar, Vaithilingam; Huy, Nguyen Quang; Li, Guoyin
2009
Dual characterizations of set containments with strict convex inequalities. Zbl 1098.90085
Goberna, M. A.; Jeyakumar, V.; Dinh, N.
2006
Sequential Lagrangian conditions for convex programs with applications to semidefinite programming. Zbl 1114.90083
Dinh, N.; Jeyakumar, V.; Lee, G. M.
2005
Farkas’ lemma: three decades of generalizations for mathematical optimization. Zbl 1330.90104
Dinh, N.; Jeyakumar, V.
2014
Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization. Zbl 1058.49013
Jeyakumar, V.; Yen, N. D.
2004
A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty. Zbl 1218.91006
Jeyakumar, V.; Li, G. Y.; Lee, G. M.
2011
Complete characterizations of global optimality for problems involving the pointwise minimum of sublinear functions. Zbl 0847.90122
Glover, B. M.; Ishizuka, Y.; Jeyakumar, V.; Tuan, H. D.
1996
Approximate generalized Hessians and Taylor’s expansions for continuously Gâteaux differentiable functions. Zbl 0931.49011
Jeyakumar, V.; Yang, X. Q.
1999
Convex composite minimization with $$C^{1,1}$$ functions. Zbl 0838.90110
Jeyakumar, V.; Yang, X. Q.
1995
Robust duality for fractional programming problems with constraint-wise data uncertainty. Zbl 1242.90252
Jeyakumar, V.; Li, G. Y.
2011
Exact SDP relaxations for classes of nonlinear semidefinite programming problems. Zbl 1287.90047
Jeyakumar, V.; Li, G.
2012
On polynomial optimization over non-compact semi-algebraic sets. Zbl 1302.90208
Jeyakumar, V.; Lasserre, J. B.; Li, G.
2014
Characterizations of generalized monotone nonsmooth continuous maps using approximate Jacobians. Zbl 0911.49014
Jeyakumar, V.; Luc, D. T.; Schaible, S.
1998
Liberating the subgradient optimality conditions from constraint qualifications. Zbl 1131.90069
Jeyakumar, V.; Wu, Z. Y.; Lee, G. M.; Dinh, N.
2006
Duality and infinite dimensional optimization. Zbl 0724.90051
Jeyakumar, V.
1990
A global approach to nonlinearly constrained best approximation. Zbl 1072.41019
Jeyakumar, V.; Mohebi, H.
2005
Sufficient conditions for global optimality of bivalent nonconvex quadratic programs with inequality constraints. Zbl 1144.90458
Wu, Z. Y.; Jeyakumar, V.; Rubinov, A. M.
2007
Necessary global optimality conditions for nonlinear programming problems with polynomial constraints. Zbl 1206.90126
Jeyakumar, V.; Li, G. Y.
2011
Robust Farkas’ lemma for uncertain linear systems with applications. Zbl 1242.90232
Jeyakumar, V.; Li, G.
2011
Stable zero duality gaps in convex programming: complete dual characterisations with applications to semidefinite programs. Zbl 1208.90134
Jeyakumar, V.; Li, G. Y.
2009
Limiting $$\varepsilon$$-subgradient characterizations of constrained best approximation. Zbl 1138.41304
Jeyakumar, V.; Mohebi, H.
2005
A general approach to dual characterizations of solvability of inequality systems with applications. Zbl 0840.52001
Rubinov, A. M.; Glover, B. M.; Jeyakumar, V.
1995
Asymptotic conditions for weak and proper optimality in infinite dimensional convex vector optimization. Zbl 0858.90110
Jeyakumar, V.; Zaffaroni, A.
1996
Convergence of the Lasserre hierarchy of SDP relaxations for convex polynomial programs without compactness. Zbl 1408.90227
Jeyakumar, V.; Phạm, T. S.; Li, G.
2014
Generalized Fenchel’s conjugation formulas and duality for abstract convex functions. Zbl 1146.49013
Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
2007
A general Farkas lemma and characterization of optimality for a nonsmooth program involving convex processes. Zbl 0616.90072
Jeyakumar, V.
1987
Dual semidefinite programs without duality gaps for a class of convex minimax programs. Zbl 1312.90087
Jeyakumar, V.; Vicente-Pérez, J.
2014
Some robust convex programs without a duality gap. Zbl 1277.90086
Jeyakumar, Vaithilingam; Li, Guo Yin; Wang, Jinhua
2013
A new class of alternative theorems for SOS-convex inequalities and robust optimization. Zbl 1338.90302
Jeyakumar, V.; Li, G.
2015
An exact formula for radius of robust feasibility of uncertain linear programs. Zbl 1373.49035
Chuong, Thai Doan; Jeyakumar, V.
2017
Nonlinear extensions of Farkas’ lemma with applications to global optimization and least squares. Zbl 0846.90098
Jeyakumar, V.; Glover, B. M.
1995
Lagrange multiplier characterizations of robust best approximations under constraint data uncertainty. Zbl 1308.41028
Jeyakumar, V.; Wang, J. H.; Li, G.
2012
Infinite-dimensional convex programming with applications to constrained approximation. Zbl 0797.90076
Jeyakumar, V.
1992
Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints. Zbl 1408.90235
Goberna, M. A.; Jeyakumar, V.; Li, G.; Linh, N.
2016
Nonlinear alternative theorems and nondifferentiable programming. Zbl 0622.90069
Jeyakumar, V.
1984
Strong duality for robust minimax fractional programming problems. Zbl 1317.90291
Jeyakumar, V.; Li, G. Y.; Srisatkunarajah, S.
2013
Simultaneous classification and feature selection via convex quadratic programming with application to HIV-associated neurocognitive disorder assessment. Zbl 1188.90235
Dunbar, Michelle; Murray, John M.; Cysique, Lucette A.; Brew, Bruce J.; Jeyakumar, Vaithilingam
2010
Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems. Zbl 1124.90022
Dinh, N.; Jeyakumar, V.; Lee, G. M.
2006
Solution point characterizations and convergence analysis of a descent algorithm for nonsmooth continuous complementarity problems. Zbl 1064.90048
Fischer, A.; Jeyakumar, V.; Luc, D. T.
2001
Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets. Zbl 1369.90136
Jeyakumar, V.; Kim, S.; Lee, G. M.; Li, G.
2016
Equivalence of a Ky Fan type minimax theorem and a Gordan type alternative theorem. Zbl 0667.49007
Craven, B. D.; Jeyakumar, V.
1986
Nonconvex theorems of the alternative and minimization. Zbl 0613.49026
Craven, B. D.; Gwinner, J.; Jeyakumar, V.
1987
Knowledge-based semidefinite linear programming classifiers. Zbl 1112.90057
Jeyakumar, V.; Ormerod, J.; Womersley, R. S.
2006
Sufficient global optimality conditions for multi-extremal smooth minimization problems with bounds and linear matrix inequality constraints. Zbl 1113.90147
Huy, N. Q.; Jeyakumar, V.; Lee, G. M.
2006
Dual conditions characterizing optimality for convex multi-objective programs. Zbl 1050.90545
Glover, B. M.; Jeyakumar, V.; Rubinov, A. M.
1999
Strong duality in robust semi-definite linear programming under data uncertainty. Zbl 1291.90164
Jeyakumar, V.; Li, G. Y.
2014
Kuhn-Tucker sufficiency for global minimum of multi-extremal mathematical programming problems. Zbl 1135.90429
Jeyakumar, V.; Srisatkunrajah, S.; Huy, N. Q.
2007
A note on strong duality in convex semidefinite optimization: necessary and sufficient conditions. Zbl 1147.90038
Jeyakumar, V.
2008
Lagrange multiplier necessary conditions for global optimality for non-convex minimization over a quadratic constraint via S-lemma. Zbl 1154.90574
Jeyakumar, V.; Srisatkunarajah, S.
2009
Constraint qualifications for convex optimization without convexity of constraints: new connections and applications to best approximation. Zbl 1374.90354
Chieu, N. H.; Jeyakumar, V.; Li, G.; Mohebi, H.
2018
First and second-order optimality conditions for convex composite multiobjective optimization. Zbl 0890.90162
Yang, X. Q.; Jeyakumar, V.
1997
The radius of robust feasibility of uncertain mathematical programs: a survey and recent developments. Zbl 07422958
Goberna, M. A.; Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2022
Exact conic programming reformulations of two-stage adjustable robust linear programs with new quadratic decision rules. Zbl 1460.90122
Woolnough, D.; Jeyakumar, V.; Li, G.
2021
Calculating radius of robust feasibility of uncertain linear conic programs via semi-definite programs. Zbl 1470.90061
Goberna, M. A.; Jeyakumar, V.; Li, G.
2021
Convexifiability of continuous and discrete nonnegative quadratic programs for gap-free duality. Zbl 1430.90467
Chieu, N. H.; Jeyakumar, V.; Li, Guoyin
2020
Generalized Farkas lemma with adjustable variables and two-stage robust linear programs. Zbl 1468.90076
Chuong, Thai Doan; Jeyakumar, Vaithilingam
2020
Characterizing best approximation from a convex set without convex representation. Zbl 1407.41012
Jeyakumar, V.; Mohebi, H.
2019
A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs. Zbl 1433.90122
Chuong, T. D.; Jeyakumar, V.; Li, G.
2019
A copositive Farkas lemma and minimally exact conic relaxations for robust quadratic optimization with binary and quadratic constraints. Zbl 1455.90125
Chieu, N. H.; Chuong, T. D.; Jeyakumar, V.; Li, G.
2019
Constraint qualifications for convex optimization without convexity of constraints: new connections and applications to best approximation. Zbl 1374.90354
Chieu, N. H.; Jeyakumar, V.; Li, G.; Mohebi, H.
2018
Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs. Zbl 1403.90606
Goberna, M. A.; Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2018
Extended trust-region problems with one or two balls: exact copositive and Lagrangian relaxations. Zbl 1421.90104
Bomze, Immanuel M.; Jeyakumar, Vaithilingam; Li, Guoyin
2018
Exact second-order cone programming relaxations for some nonconvex minimax quadratic optimization problems. Zbl 1396.90064
Jeyakumar, V.; Li, G.
2018
Tight SDP relaxations for a class of robust SOS-convex polynomial programs without the Slater condition. Zbl 1429.90085
Chuong, T. D.; Jeyakumar, V.
2018
Generalized Lagrangian duality for nonconvex polynomial programs with polynomial multipliers. Zbl 1433.90158
Chuong, T. D.; Jeyakumar, V.
2018
An exact formula for radius of robust feasibility of uncertain linear programs. Zbl 1373.49035
Chuong, Thai Doan; Jeyakumar, V.
2017
A generalized Farkas lemma with a numerical certificate and linear semi-infinite programs with SDP duals. Zbl 1352.90060
Chuong, T. D.; Jeyakumar, V.
2017
Finding robust global optimal values of bilevel polynomial programs with uncertain linear constraints. Zbl 1370.49017
Chuong, Thai Doan; Jeyakumar, V.
2017
Convergent conic linear programming relaxations for cone convex polynomial programs. Zbl 1409.90131
Chuong, T. D.; Jeyakumar, V.
2017
Exact conic programming relaxations for a class of convex polynomial cone programs. Zbl 1388.90093
Jeyakumar, Vaithilingam; Li, Guoyin
2017
Convergent hierarchy of SDP relaxations for a class of semi-infinite convex polynomial programs and applications. Zbl 1426.90242
Chuong, T. D.; Jeyakumar, V.
2017
A convergent hierarchy of SDP relaxations for a class of hard robust global polynomial optimization problems. Zbl 1409.90182
Chieu, N. H.; Jeyakumar, V.; Li, G.
2017
Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints. Zbl 1408.90235
Goberna, M. A.; Jeyakumar, V.; Li, G.; Linh, N.
2016
Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets. Zbl 1369.90136
Jeyakumar, V.; Kim, S.; Lee, G. M.; Li, G.
2016
Robust global error bounds for uncertain linear inequality systems with applications. Zbl 1348.49041
Chuong, T. D.; Jeyakumar, V.
2016
Characterizing robust local error bounds for linear inequality systems under data uncertainty. Zbl 1328.49026
Chuong, T. D.; Jeyakumar, V.
2016
Convergent semidefinite programming relaxations for global bilevel polynomial optimization problems. Zbl 1333.90088
Jeyakumar, V.; Lasserre, J. B.; Li, G.; Phạm, T. S.
2016
Sums of squares characterizations of containment of convex semialgebraic sets. Zbl 1333.14058
Jeyakumar, V.; Lee, G. M.; Lee, J. H.
2016
Generalized Farkas’ lemma and gap-free duality for minimax DC optimization with polynomials and robust quadratic optimization. Zbl 1346.90808
Jeyakumar, V.; Lee, G. M.; Linh, N. T. H.
2016
Generalized SOS-convexity and strong duality with SDP dual programs in polynomial optimization. Zbl 1334.26024
Jeyakumar, Vaithilingam; Lee, Gue Myung; Lee, Jae Hyoung
2016
Robust solutions to multi-objective linear programs with uncertain data. Zbl 1341.90124
Goberna, M. A.; Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2015
Characterizing robust solution sets of convex programs under data uncertainty. Zbl 1307.90136
Jeyakumar, V.; Lee, G. M.; Li, G.
2015
Robust SOS-convex polynomial optimization problems: exact SDP relaxations. Zbl 1338.90452
Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2015
A new class of alternative theorems for SOS-convex inequalities and robust optimization. Zbl 1338.90302
Jeyakumar, V.; Li, G.
2015
A bilevel Farkas lemma to characterizing global solutions of a class of bilevel polynomial programs. Zbl 1408.90226
Jeyakumar, V.; Li, G.
2015
Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization. Zbl 1297.90105
Jeyakumar, V.; Li, G. Y.
2014
Robust solutions of multiobjective linear semi-infinite programs under constraint data uncertainty. Zbl 1325.90081
Goberna, M. A.; Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2014
Farkas’ lemma: three decades of generalizations for mathematical optimization. Zbl 1330.90104
Dinh, N.; Jeyakumar, V.
2014
On polynomial optimization over non-compact semi-algebraic sets. Zbl 1302.90208
Jeyakumar, V.; Lasserre, J. B.; Li, G.
2014
Convergence of the Lasserre hierarchy of SDP relaxations for convex polynomial programs without compactness. Zbl 1408.90227
Jeyakumar, V.; Phạm, T. S.; Li, G.
2014
Dual semidefinite programs without duality gaps for a class of convex minimax programs. Zbl 1312.90087
Jeyakumar, V.; Vicente-Pérez, J.
2014
Strong duality in robust semi-definite linear programming under data uncertainty. Zbl 1291.90164
Jeyakumar, V.; Li, G. Y.
2014
Support vector machine classifiers with uncertain knowledge sets via robust optimization. Zbl 1298.65104
Jeyakumar, V.; Li, G.; Suthaharan, S.
2014
Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations. Zbl 1319.90052
Jeyakumar, V.; Li, G.; Srisatkunarajah, S.
2014
Rejoinder on: “Farkas’ lemma: three decades of generalizations for mathematical optimization”. Zbl 1304.90192
Dinh, N.; Jeyakumar, V.
2014
Robust linear semi-infinite programming duality under uncertainty. Zbl 1282.90204
Goberna, M. A.; Jeyakumar, V.; Li, G.; López, M. A.
2013
Robust duality in parametric convex optimization. Zbl 1327.90195
Boţ, R. I.; Jeyakumar, V.; Li, G. Y.
2013
Some robust convex programs without a duality gap. Zbl 1277.90086
Jeyakumar, Vaithilingam; Li, Guo Yin; Wang, Jinhua
2013
Strong duality for robust minimax fractional programming problems. Zbl 1317.90291
Jeyakumar, V.; Li, G. Y.; Srisatkunarajah, S.
2013
Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty. Zbl 1288.90058
Jeyakumar, V.; Li, G. Y.
2013
Robust best approximation with interpolation constraints under ellipsoidal uncertainty: strong duality and nonsmooth Newton methods. Zbl 1263.41016
Jeyakumar, V.; Li, G. Y.; Mordukhovich, B. S.; Wang, J. H.
2013
Robust duality for generalized convex programming problems under data uncertainty. Zbl 1254.90154
Jeyakumar, V.; Li, G.; Lee, G. M.
2012
Exact SDP relaxations for classes of nonlinear semidefinite programming problems. Zbl 1287.90047
Jeyakumar, V.; Li, G.
2012
Lagrange multiplier characterizations of robust best approximations under constraint data uncertainty. Zbl 1308.41028
Jeyakumar, V.; Wang, J. H.; Li, G.
2012
Robust conjugate duality for convex optimization under uncertainty with application to data classification. Zbl 1233.90231
Li, G. Y.; Jeyakumar, V.; Lee, G. M.
2011
A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty. Zbl 1218.91006
Jeyakumar, V.; Li, G. Y.; Lee, G. M.
2011
Robust duality for fractional programming problems with constraint-wise data uncertainty. Zbl 1242.90252
Jeyakumar, V.; Li, G. Y.
2011
Necessary global optimality conditions for nonlinear programming problems with polynomial constraints. Zbl 1206.90126
Jeyakumar, V.; Li, G. Y.
2011
Robust Farkas’ lemma for uncertain linear systems with applications. Zbl 1242.90232
Jeyakumar, V.; Li, G.
2011
Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems. Zbl 1230.90145
Jeyakumar, V.; Li, Guoyin
2011
Strong duality in robust convex programming: complete characterizations. Zbl 1228.90075
Jeyakumar, V.; Li, G. Y.
2010
Characterizing robust set containments and solutions of uncertain linear programs without qualifications. Zbl 1220.90067
Jeyakumar, V.; Li, Guoyin
2010
Simultaneous classification and feature selection via convex quadratic programming with application to HIV-associated neurocognitive disorder assessment. Zbl 1188.90235
Dunbar, Michelle; Murray, John M.; Cysique, Lucette A.; Brew, Bruce J.; Jeyakumar, Vaithilingam
2010
Stability, stabilization and duality for linear time-varying systems. Zbl 1209.93123
Phat, Vu N.; Jeyakumar, V.
2010
Glogal optimality conditions for classes of non-convex multi-objective quadratic optimization problems. Zbl 1236.90111
Jeyakumar, V.; Lee, G. M.; Li, G.
2010
New strong duality results for convex programs with separable constraints. Zbl 1229.90124
Jeyakumar, V.; Li, G.
2010
Alternative theorems for quadratic inequality systems and global quadratic optimization. Zbl 1197.90315
Jeyakumar, V.; Lee, G. M.; Li, G. Y.
2009
Necessary and sufficient conditions for $$S$$-lemma and nonconvex quadratic optimization. Zbl 1273.90141
Jeyakumar, Vaithilingam; Huy, Nguyen Quang; Li, Guoyin
2009
Stable zero duality gaps in convex programming: complete dual characterisations with applications to semidefinite programs. Zbl 1208.90134
Jeyakumar, V.; Li, G. Y.
2009
Lagrange multiplier necessary conditions for global optimality for non-convex minimization over a quadratic constraint via S-lemma. Zbl 1154.90574
Jeyakumar, V.; Srisatkunarajah, S.
2009
Farkas’ lemma for separable sublinear inequalities without qualifications. Zbl 1206.90082
Jeyakumar, V.; Li, G. Y.
2009
New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs. Zbl 1239.90084
Jeyakumar, Vaithilingam; Li, Guo Yin
2009
Qualification-free optimality conditions for convex programs with separable inequality constraints. Zbl 1182.49016
Li, G. Y.; Jeyakumar, V.
2009
New sufficiency for global optimality and duality of mathematical programming problems via underestimators. Zbl 1191.90067
Jeyakumar, V.; Srisatkunarajah, S.
2009
Geometric conditions for Kuhn-Tucker sufficiency of global optimality in mathematical programming. Zbl 1154.90590
Jeyakumar, V.; Srisatkunarajah, S.
2009
New Kuhn-Tucker sufficiency for global optimality via convexification. Zbl 1192.90201
Jeyakumar, V.; Lee, G. M.; Srisatkunarajah, S.
2009
A note on sufficient global optimality conditions for fixed charge quadratic programs. Zbl 1179.90310
Jeyakumar, V.; Srisatkunarajah, S.
2009
Nonsmooth vector functions and continuous optimization. Zbl 1138.90002
Jeyakumar, V.; Dinh The Luc
2008
Necessary and sufficient constraint qualifications for solvability of systems of infinite convex inequalities. Zbl 1145.90051
Goberna, M. A.; Jeyakumar, V.; López, M. A.
2008
Constraint qualifications characterizing Lagrangian duality in convex optimization. Zbl 1194.90069
Jeyakumar, V.
2008
Complete characterizations of stable Farkas’ lemma and cone-convex programming duality. Zbl 1145.90074
Jeyakumar, V.; Lee, G. M.
2008
A note on strong duality in convex semidefinite optimization: necessary and sufficient conditions. Zbl 1147.90038
Jeyakumar, V.
2008
Global minimization of difference of quadratic and convex functions over box or binary constraints. Zbl 1161.90465
Jeyakumar, V.; Huy, N. Q.
2008
Necessary and sufficient conditions for Farkas’ Lemma for cone systems and second-order cone programming duality. Zbl 1245.90141
Jeyakumar, V.; Kum, S.; Lee, G. M.
2008
Unified global optimality conditions for smooth minimization problems with mixed variables. Zbl 1153.90544
Jeyakumar, Vaithilingam; Srisatkunarajah, Sivakolundu; Huy, Nguyen Quang
2008
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions. Zbl 1206.90178
Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
2007
Sufficient conditions for global optimality of bivalent nonconvex quadratic programs with inequality constraints. Zbl 1144.90458
Wu, Z. Y.; Jeyakumar, V.; Rubinov, A. M.
2007
Generalized Fenchel’s conjugation formulas and duality for abstract convex functions. Zbl 1146.49013
Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
2007
Kuhn-Tucker sufficiency for global minimum of multi-extremal mathematical programming problems. Zbl 1135.90429
Jeyakumar, V.; Srisatkunrajah, S.; Huy, N. Q.
2007
Conditions for global optimality of quadratic minimization problems with LMI constraints. Zbl 1118.41018
Jeyakumar, Vaithilingam; Wu, Zhiyou
2007
A dual criterion for maximal monotonicity of composition operators. Zbl 1133.47039
Jeyakumar, V.; Wu, Z. Y.
2007
Characterizations of solution sets of convex vector minimization problems. Zbl 1103.90090
Jeyakumar, V.; Lee, G. M.; Dinh, N.
2006
Sufficient global optimality conditions for non-convex quadratic minimization problems with box constraints. Zbl 1131.90060
Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
2006
The strong conical hull intersection property for convex programming. Zbl 1134.90462
Jeyakumar, V.
2006
Necessary and sufficient conditions for stable conjugate duality. Zbl 1091.49031
Burachik, R. S.; Jeyakumar, V.; Wu, Z.-Y.
2006
Dual characterizations of set containments with strict convex inequalities. Zbl 1098.90085
Goberna, M. A.; Jeyakumar, V.; Dinh, N.
2006
Liberating the subgradient optimality conditions from constraint qualifications. Zbl 1131.90069
Jeyakumar, V.; Wu, Z. Y.; Lee, G. M.; Dinh, N.
2006
Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems. Zbl 1124.90022
Dinh, N.; Jeyakumar, V.; Lee, G. M.
2006
Knowledge-based semidefinite linear programming classifiers. Zbl 1112.90057
Jeyakumar, V.; Ormerod, J.; Womersley, R. S.
2006
Sufficient global optimality conditions for multi-extremal smooth minimization problems with bounds and linear matrix inequality constraints. Zbl 1113.90147
Huy, N. Q.; Jeyakumar, V.; Lee, G. M.
2006
A qualification free sequential Pshenichnyi-Rockafellar lemma and convex semidefinite. Zbl 1109.49015
Jeyakumar, V.; Wu, Z. Y.
2006
...and 67 more Documents
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### Cited by 1,060 Authors

 123 Jeyakumar, Vaithilingam 50 Li, Guoyin 37 Lee, Gue Myung 37 Yang, Xiaoqi 33 Antczak, Tadeusz 32 Goberna, Miguel Angel 32 Mishra, Shashi Kant 25 Chuong, Thai Doan 23 Boţ, Radu Ioan 23 Yao, Jen-Chih 22 López-Cerdá, Marco Antonio 22 Wu, Zhiyou 19 Mohebi, Hossein 19 Yang, Xinmin 18 Kuroiwa, Daishi 16 Gadhi, Nazih Abderrazzak 16 Kim, Do Sang 16 Lee, Jae Hyoung 16 Wanka, Gert 15 Flores-Bazán, Fabián 15 Sun, Xiangkai 15 Suzuki, Satoshi 15 Wang, Shouyang 15 Zalmai, G. J. 14 Jayswal, Anurag 14 Volle, Michel 13 Nobakhtian, Soghra 13 Soleimani-damaneh, Majid 13 Teo, Kok Lay 12 Ahmad, Izhar 12 Fang, Donghui 12 Nguyen Dong Yen 11 Dempe, Stephan 11 Dinh The Luc 11 Ivanov, Vsevolod Ivanov 10 Rubinov, Alexander M. 10 Salahi, Maziar 10 Suneja, Surjeet Kaur 10 Wangkeeree, Rabian 9 Chen, Jiawei 9 Craven, Bruce Desmond 9 Do Van Luu 9 Huy, Nguyen Quang 9 Jiao, Liguo 9 Li, Shengjie 9 Mehra, Aparna 8 Bhatia, Davinder 8 Chieu, Nguyen Huy 8 Long, Xianjun 8 Noor, Muhammad Aslam 8 Pastor, Karel 8 Penot, Jean-Paul 8 Son, Ta Quang 8 Srisatkunarajah, Sivakolundu 8 Stancu-Minasian, Ioan M. 7 Ansari, Qamrul Hasan 7 Bai, Fusheng 7 Ginchev, Ivan G. 7 Kassay, Gábor 7 Kohli, Bhawna 7 Liu, Sanyang 7 Long, Dang Hai 7 Mordukhovich, Boris S. 7 Movahedian, Nooshin 7 Ng, Kung-Fu 7 Phan Quôc Khánh 7 Vicente-Pérez, José 6 Burachik, Regina Sandra 6 Chen, Chunrong 6 Chen, Zhe 6 Correa, Rafael 6 Csetnek, Ernö Robert 6 Grad, Sorin-Mihai 6 Kabgani, Alireza 6 Kim, Moon Hee 6 Kostyukova, Olga Ivanova 6 Lafhim, Lahoussine 6 Lara, Felipe 6 Li, Jun 6 Mastroeni, Giandomenico 6 Pham Huu Sach 6 Preda, Vasile C. 6 Rojas-Medar, Marko Antonio 6 Roshchina, Vera 6 Rufián-Lizana, Antonio 6 Schöbel, Anita 6 Sisarat, Nithirat 6 Tang, Liping 6 Tchemisova, Tatiana V. 6 Tian, Jing 6 Verma, Ram U. 6 Wu, Di 6 Zafarani, Jafar 6 Zhao, Kequan 5 Al-Homidan, Suliman S. 5 Bector, C. R. 5 Chen, Jein-Shan 5 Doagooei, Ali Reza 5 El Idrissi, Mohammed 5 Guerraggio, Angelo ...and 960 more Authors
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### Cited in 155 Serials

 198 Journal of Optimization Theory and Applications 124 Optimization 104 Journal of Global Optimization 83 Journal of Mathematical Analysis and Applications 71 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 53 Optimization Letters 50 European Journal of Operational Research 46 Mathematical Programming. Series A. Series B 31 Numerical Functional Analysis and Optimization 30 SIAM Journal on Optimization 22 Journal of Inequalities and Applications 20 Set-Valued and Variational Analysis 19 Operations Research Letters 17 Positivity 15 Annals of Operations Research 15 Journal of Industrial and Management Optimization 14 Applied Mathematics and Computation 14 Opsearch 14 Applied Mathematics Letters 14 Top 13 Computers & Mathematics with Applications 11 Journal of Computational and Applied Mathematics 11 Computational Optimization and Applications 11 Mathematical Methods of Operations Research 9 Vietnam Journal of Mathematics 9 Journal of Applied Mathematics 9 Nonlinear Analysis. Theory, Methods & Applications 8 Journal of Information & Optimization Sciences 8 Set-Valued Analysis 8 Journal of Applied Mathematics and Computing 7 Applied Mathematics and Optimization 7 Filomat 6 Bulletin of the Australian Mathematical Society 6 Acta Mathematicae Applicatae Sinica. English Series 5 Asia-Pacific Journal of Operational Research 5 Linear Algebra and its Applications 5 Applied Mathematics. Series B (English Edition) 5 Abstract and Applied Analysis 5 RAIRO. Operations Research 5 Journal of Systems Science and Complexity 5 Numerical Algebra, Control and Optimization 5 Journal of the Operations Research Society of China 4 Applicable Analysis 4 Fuzzy Sets and Systems 4 Journal of Approximation Theory 4 Rendiconti del Circolo Matemàtico di Palermo. Serie II 4 Bulletin of the Iranian Mathematical Society 4 Mathematical and Computer Modelling 4 Applications of Mathematics 4 Computational and Applied Mathematics 4 Journal of Applied Analysis 4 Taiwanese Journal of Mathematics 4 Fixed Point Theory and Applications 4 Journal of Nonlinear Analysis and Optimization: Theory & Applications 3 Computer Methods in Applied Mechanics and Engineering 3 Kybernetika 3 Mathematics of Operations Research 3 International Journal of Computer Mathematics 3 Journal of Convex Analysis 3 INFORMS Journal on Computing 3 Optimization Methods & Software 3 The ANZIAM Journal 3 Central European Journal of Mathematics 3 Thai Journal of Mathematics 3 Open Mathematics 3 Minimax Theory and its Applications 3 AIMS Mathematics 3 SN Operations Research Forum 2 Archiv der Mathematik 2 Automatica 2 International Journal of Mathematics and Mathematical Sciences 2 Proceedings of the American Mathematical Society 2 Neural Networks 2 YUJOR. Yugoslav Journal of Operations Research 2 ZOR. Zeitschrift für Operations Research 2 Journal of Mathematical Sciences (New York) 2 Fractals 2 Mathematical Problems in Engineering 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Discrete Dynamics in Nature and Society 2 Journal of Interdisciplinary Mathematics 2 Acta Mathematica Sinica. English Series 2 Optimization and Engineering 2 Decisions in Economics and Finance 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 4OR 2 Nonlinear Analysis. Hybrid Systems 2 Advances in Operations Research 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Mathematical Sciences 2 Journal of Function Spaces 2 Journal of Nonlinear and Variational Analysis 1 International Journal of Control 1 International Journal of Engineering Science 1 Mathematical Methods in the Applied Sciences 1 Rocky Mountain Journal of Mathematics 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Acta Mathematica Vietnamica 1 Calcolo 1 Information Sciences ...and 55 more Serials
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### Cited in 39 Fields

 1,165 Operations research, mathematical programming (90-XX) 501 Calculus of variations and optimal control; optimization (49-XX) 138 Real functions (26-XX) 90 Numerical analysis (65-XX) 55 Operator theory (47-XX) 50 Convex and discrete geometry (52-XX) 48 Functional analysis (46-XX) 26 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 24 Global analysis, analysis on manifolds (58-XX) 20 Approximations and expansions (41-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 14 General topology (54-XX) 13 Computer science (68-XX) 9 Systems theory; control (93-XX) 7 Algebraic geometry (14-XX) 7 Statistics (62-XX) 7 Mechanics of deformable solids (74-XX) 5 Ordinary differential equations (34-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Difference and functional equations (39-XX) 3 Biology and other natural sciences (92-XX) 2 Field theory and polynomials (12-XX) 2 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Information and communication theory, circuits (94-XX)