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## 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 · Wikidata · ORCID · dblp
 Documents Indexed: 173 Publications since 1984, including 2 Books
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#### Co-Authors

 21 single-authored 49 Li, Guoyin 22 Lee, Gue Myung 11 Chuong, Thai Doan 10 Wu, Zhiyou 9 Dinh The Luc 9 Rubinov, Alexander M. 9 Srisatkunarajah, Sivakolundu 8 Glover, Bevil Milton 7 Goberna, Miguel Angel 7 Huy, Nguyen Quang 6 Dinh, Ngo Van 6 Yang, Xiaoqi 5 Gwinner, Joachim 5 Vicente-Pérez, José 4 Burachik, Regina Sandra 4 Chieu, Nguyen Huy 4 Mohebi, Hossein 4 Oettli, Werner 3 Craven, Bruce Desmond 3 Glover, Barney M. 3 Wang, Jinhua 2 Dinh, Nguyen Pham 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 Dinh, Nam T. 1 Dunbar, Michelle 1 Fischer, Andrew F. 1 Kim, Sangyeon 1 Kum, Sangho 1 Li, Gongquan 1 Linh, Nguyen Thi Hoai 1 Linh, Nguyen Thi Hong 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 Womersley, Robert S. 1 Woolnough, D. 1 Nguyen Dong Yen 1 Zaffaroni, Alberto
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#### Serials

 23 Journal of Optimization Theory and Applications 13 Journal of Global Optimization 12 Mathematical Programming. Series A. Series B 12 SIAM Journal on Optimization 10 Operations Research Letters 10 Optimization 9 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

 158 Operations research, mathematical programming (90-XX) 65 Calculus of variations and optimal control; optimization (49-XX) 12 Approximations and expansions (41-XX) 11 Real functions (26-XX) 11 Numerical analysis (65-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

162 Publications have been cited 2,627 times in 1,196 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
New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs. Zbl 1046.90059
Jeyakumar, V.; Lee, G. M.; Dinh, N.
2003
A class of nonconvex functions and mathematical programming. Zbl 0639.90082
Weir, T.; Jeyakumar, V.
1988
Nonsmooth calculus, minimality, and monotonicity of convexificators. Zbl 0956.90033
Jeyakumar, V.; Luc, D. T.
1999
Strong and weak invexity in mathematical programming. Zbl 0566.90086
Jeyakumar, V.
1985
Strong duality in robust convex programming: complete characterizations. Zbl 1228.90075
Jeyakumar, V.; Li, G. Y.
2010
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions. Zbl 1206.90178
Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
2007
Generalizations of Slater’s constraint qualification for infinite convex programs. Zbl 0771.90078
Jeyakumar, V.; Wolkowicz, Henry
1992
Convexlike alternative theorems and mathematical programming. Zbl 0581.90079
Jeyakumar, V.
1985
Characterizing set containments involving infinite convex constraints and reverse-convex constraints. Zbl 1038.90061
Jeyakumar, V.
2003
A solvability theorem for a class of quasiconvex mappings with applications to optimization. Zbl 0791.46002
Jeyakumar, V.; Oettli, W.; Natividad, M.
1993
Nonsmooth vector functions and continuous optimization. Zbl 1138.90002
Jeyakumar, V.; Dinh The Luc
2008
Convex composite multi-objective nonsmooth programming. Zbl 0789.90068
Jeyakumar, V.; Yang, X. Q.
1993
A new geometric condition for Fenchel’s duality in infinite dimensional spaces. Zbl 1093.90077
Burachik, Regina Sandra; Jeyakumar, Vaithilingam
2005
Hunting for a smaller convex subdifferential. Zbl 0872.90083
Demyanov, V. F.; Jeyakumar, V.
1997
On characterizing the solution sets of pseudolinear programs. Zbl 0840.90118
Jeyakumar, V.; Yang, X. Q.
1995
A generalization of a minimax theorem of Fan via a theorem of the alternative. Zbl 0563.49006
Jeyakumar, V.
1986
Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization. Zbl 1297.90105
Jeyakumar, V.; Li, G. Y.
2014
Alternative theorems for quadratic inequality systems and global quadratic optimization. Zbl 1197.90315
Jeyakumar, V.; Lee, G. M.; Li, G. Y.
2009
A dual condition for the convex subdifferential sum formula with applications. Zbl 1098.49017
Burachik, R. S.; Jeyakumar, V.
2005
Generalized second-order directional derivatives and optimization with $$C^{1,1}$$ functions. Zbl 0814.49012
Yang, X. Q.; Jeyakumar, V.
1992
Zero duality gaps in infinite-dimensional programming. Zbl 0687.90077
Jeyakumar, V.; Wolkowicz, H.
1990
Robust solutions to multi-objective linear programs with uncertain data. Zbl 1341.90124
Goberna, M. A.; Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2015
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
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
Constraint qualifications characterizing Lagrangian duality in convex optimization. Zbl 1194.90069
Jeyakumar, V.
2008
Characterizing robust set containments and solutions of uncertain linear programs without qualifications. Zbl 1220.90067
Jeyakumar, V.; Li, Guoyin
2010
Composite nonsmooth programming with Gâteaux differentiability. Zbl 0752.90067
Jeyakumar, V.
1991
Lagrange multiplier conditions characterizing the optimal solution sets of cone-constrained convex programs. Zbl 1114.90091
Jeyakumar, V.; Lee, G. M.; Dinh, N.
2004
Inequality systems and global optimization. Zbl 0856.90128
Jeyakumar, V.; Rubinov, A. M.; Glover, B. M.; Ishizuka, Y.
1996
Asymptotic dual conditions characterizing optimality for infinite convex programs. Zbl 0901.90158
Jeyakumar, V.
1997
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
Inequality systems and optimization. Zbl 0734.90089
Jeyakumar, V.; Gwinner, J.
1991
The strong conical hull intersection property for convex programming. Zbl 1134.90462
Jeyakumar, V.
2006
Robust linear semi-infinite programming duality under uncertainty. Zbl 1282.90204
Goberna, M. A.; Jeyakumar, V.; Li, G.; López, M. A.
2013
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
Necessary and sufficient conditions for stable conjugate duality. Zbl 1091.49031
Burachik, R. S.; Jeyakumar, V.; Wu, Z.-Y.
2006
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
A sharp Lagrange multiplier rule for nonsmooth mathematical programming problems involving equality constraints. Zbl 1047.90075
Wang, Xiang; Jeyakumar, V.
2000
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
Necessary and sufficient conditions for $$S$$-lemma and nonconvex quadratic optimization. Zbl 1273.90141
Jeyakumar, Vaithilingam; Huy, Nguyen Quang; Li, Guoyin
2009
A simple closure condition for the normal cone intersection formula. Zbl 1065.46055
Burachik, Regina Sandra; Jeyakumar, Vaithilingam
2005
Sequential Lagrangian conditions for convex programs with applications to semidefinite programming. Zbl 1114.90083
Dinh, N.; Jeyakumar, V.; Lee, G. M.
2005
Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization. Zbl 1058.49013
Jeyakumar, V.; Yen, N. D.
2004
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
Characterizing robust solution sets of convex programs under data uncertainty. Zbl 1307.90136
Jeyakumar, V.; Lee, G. M.; Li, G.
2015
Dual characterizations of set containments with strict convex inequalities. Zbl 1098.90085
Goberna, M. A.; Jeyakumar, V.; Dinh, N.
2006
Convex composite minimization with $$C^{1,1}$$ functions. Zbl 0838.90110
Jeyakumar, V.; Yang, X. Q.
1995
Robust SOS-convex polynomial optimization problems: exact SDP relaxations. Zbl 1338.90452
Jeyakumar, V.; Li, G.; Vicente-Pérez, J.
2015
Robust duality in parametric convex optimization. Zbl 1327.90195
Boţ, R. I.; Jeyakumar, V.; Li, G. Y.
2013
Exact SDP relaxations for classes of nonlinear semidefinite programming problems. Zbl 1287.90047
Jeyakumar, V.; Li, G.
2012
Approximate generalized Hessians and Taylor’s expansions for continuously Gâteaux differentiable functions. Zbl 0931.49011
Jeyakumar, V.; Yang, X. Q.
1999
On polynomial optimization over non-compact semi-algebraic sets. Zbl 1302.90208
Jeyakumar, V.; Lasserre, J. B.; Li, G.
2014
Farkas’ lemma: three decades of generalizations for mathematical optimization. Zbl 1330.90104
Dinh, N.; Jeyakumar, V.
2014
Robust duality for generalized convex programming problems under data uncertainty. Zbl 1254.90154
Jeyakumar, V.; Li, G.; Lee, G. M.
2012
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
Necessary global optimality conditions for nonlinear programming problems with polynomial constraints. Zbl 1206.90126
Jeyakumar, V.; Li, G. Y.
2011
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
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 new class of alternative theorems for SOS-convex inequalities and robust optimization. Zbl 1338.90302
Jeyakumar, V.; Li, G.
2015
Robust duality for fractional programming problems with constraint-wise data uncertainty. Zbl 1242.90252
Jeyakumar, V.; Li, G. Y.
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
Characterizations of generalized monotone nonsmooth continuous maps using approximate Jacobians. Zbl 0911.49014
Jeyakumar, V.; Luc, D. T.; Schaible, S.
1998
Asymptotic conditions for weak and proper optimality in infinite dimensional convex vector optimization. Zbl 0858.90110
Jeyakumar, V.; Zaffaroni, A.
1996
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
Robust Farkas’ lemma for uncertain linear systems with applications. Zbl 1242.90232
Jeyakumar, V.; Li, G.
2011
Nonlinear extensions of Farkas’ lemma with applications to global optimization and least squares. Zbl 0846.90098
Jeyakumar, V.; Glover, B. M.
1995
A general Farkas lemma and characterization of optimality for a nonsmooth program involving convex processes. Zbl 0616.90072
Jeyakumar, V.
1987
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
Limiting $$\varepsilon$$-subgradient characterizations of constrained best approximation. Zbl 1138.41304
Jeyakumar, V.; Mohebi, H.
2005
Infinite-dimensional convex programming with applications to constrained approximation. Zbl 0797.90076
Jeyakumar, V.
1992
Some robust convex programs without a duality gap. Zbl 1277.90086
Jeyakumar, Vaithilingam; Li, Guo Yin; Wang, Jinhua
2013
Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems. Zbl 1124.90022
Dinh, N.; Jeyakumar, V.; Lee, G. M.
2006
A global approach to nonlinearly constrained best approximation. Zbl 1072.41019
Jeyakumar, V.; Mohebi, H.
2005
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
First and second-order optimality conditions for convex composite multiobjective optimization. Zbl 0890.90162
Yang, X. Q.; Jeyakumar, V.
1997
Nonlinear alternative theorems and nondifferentiable programming. Zbl 0622.90069
Jeyakumar, V.
1984
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
Dual conditions characterizing optimality for convex multi-objective programs. Zbl 1050.90545
Glover, B. M.; Jeyakumar, V.; Rubinov, A. M.
1999
A Farkas lemma for difference sublinear systems and quasidifferentiable programming. Zbl 0804.49015
Glover, B. M.; Jeyakumar, V.; Oettli, W.
1994
Nonconvex theorems of the alternative and minimization. Zbl 0613.49026
Craven, B. D.; Gwinner, J.; Jeyakumar, V.
1987
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
Strong duality in robust semi-definite linear programming under data uncertainty. Zbl 1291.90164
Jeyakumar, V.; Li, G. Y.
2014
Strong duality for robust minimax fractional programming problems. Zbl 1317.90291
Jeyakumar, V.; Li, G. Y.; Srisatkunarajah, S.
2013
Lagrange multiplier characterizations of robust best approximations under constraint data uncertainty. Zbl 1308.41028
Jeyakumar, V.; Wang, J. H.; Li, G.
2012
Global minimization of difference of quadratic and convex functions over box or binary constraints. Zbl 1161.90465
Jeyakumar, V.; Huy, N. Q.
2008
A note on strong duality in convex semidefinite optimization: necessary and sufficient conditions. Zbl 1147.90038
Jeyakumar, V.
2008
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
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
Knowledge-based semidefinite linear programming classifiers. Zbl 1112.90057
Jeyakumar, V.; Ormerod, J.; Womersley, R. S.
2006
An open mapping theorem using unbounded generalized Jacobians. Zbl 1035.49016
Jeyakumar, V.; Luc, D. T.
2002
Characterizing global optimality for DC optimization problems under convex inequality constraints. Zbl 0855.90100
Jeyakumar, V.; Glover, B. M.
1996
Equivalence of a Ky Fan type minimax theorem and a Gordan type alternative theorem. Zbl 0667.49007
Craven, B. D.; Jeyakumar, V.
1986
Convexifiability of continuous and discrete nonnegative quadratic programs for gap-free duality. Zbl 1430.90467
Chieu, N. H.; Jeyakumar, V.; Li, Guoyin
2020
A copositive Farkas lemma and minimally exact conic relaxations for robust quadratic optimization with binary and quadratic constraints. Zbl 07165838
Chieu, N. H.; Chuong, T. D.; Jeyakumar, V.; Li, G.
2019
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
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
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
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
Exact second-order cone programming relaxations for some nonconvex minimax quadratic optimization problems. Zbl 1396.90064
Jeyakumar, V.; Li, G.
2018
Generalized Lagrangian duality for nonconvex polynomial programs with polynomial multipliers. Zbl 1433.90158
Chuong, T. D.; Jeyakumar, V.
2018
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
An exact formula for radius of robust feasibility of uncertain linear programs. Zbl 1373.49035
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
Finding robust global optimal values of bilevel polynomial programs with uncertain linear constraints. Zbl 1370.49017
Chuong, Thai Doan; 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
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
Convergent semidefinite programming relaxations for global bilevel polynomial optimization problems. Zbl 1333.90088
Jeyakumar, V.; Lasserre, J. B.; Li, G.; Phạm, T. S.
2016
Robust global error bounds for uncertain linear inequality systems with applications. Zbl 1348.49041
Chuong, T. D.; Jeyakumar, V.
2016
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
Characterizing robust local error bounds for linear inequality systems under data uncertainty. Zbl 1328.49026
Chuong, T. D.; Jeyakumar, V.
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
On polynomial optimization over non-compact semi-algebraic sets. Zbl 1302.90208
Jeyakumar, V.; Lasserre, J. B.; Li, G.
2014
Farkas’ lemma: three decades of generalizations for mathematical optimization. Zbl 1330.90104
Dinh, N.; Jeyakumar, V.
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
Exact SDP relaxations for classes of nonlinear semidefinite programming problems. Zbl 1287.90047
Jeyakumar, V.; Li, G.
2012
Robust duality for generalized convex programming problems under data uncertainty. Zbl 1254.90154
Jeyakumar, V.; Li, G.; Lee, G. M.
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
Necessary global optimality conditions for nonlinear programming problems with polynomial constraints. Zbl 1206.90126
Jeyakumar, V.; Li, G. Y.
2011
Robust duality for fractional programming problems with constraint-wise data uncertainty. Zbl 1242.90252
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
Qualification-free optimality conditions for convex programs with separable inequality constraints. Zbl 1182.49016
Li, G. Y.; Jeyakumar, V.
2009
New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs. Zbl 1239.90084
Jeyakumar, Vaithilingam; Li, Guo Yin
2009
Farkas’ lemma for separable sublinear inequalities without qualifications. Zbl 1206.90082
Jeyakumar, V.; Li, G. Y.
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
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
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
Global minimization of difference of quadratic and convex functions over box or binary constraints. Zbl 1161.90465
Jeyakumar, V.; Huy, N. Q.
2008
A note on strong duality in convex semidefinite optimization: necessary and sufficient conditions. Zbl 1147.90038
Jeyakumar, V.
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
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
Characterizations of solution sets of convex vector minimization problems. Zbl 1103.90090
Jeyakumar, V.; Lee, G. M.; Dinh, N.
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
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
Knowledge-based semidefinite linear programming classifiers. Zbl 1112.90057
Jeyakumar, V.; Ormerod, J.; Womersley, R. S.
2006
A qualification free sequential Pshenichnyi-Rockafellar lemma and convex semidefinite. Zbl 1109.49015
Jeyakumar, V.; Wu, Z. Y.
2006
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
A simple closure condition for the normal cone intersection formula. Zbl 1065.46055
Burachik, Regina Sandra; Jeyakumar, Vaithilingam
2005
Sequential Lagrangian conditions for convex programs with applications to semidefinite programming. Zbl 1114.90083
Dinh, N.; Jeyakumar, V.; Lee, G. M.
2005
Limiting $$\varepsilon$$-subgradient characterizations of constrained best approximation. Zbl 1138.41304
Jeyakumar, V.; Mohebi, H.
2005
A global approach to nonlinearly constrained best approximation. Zbl 1072.41019
Jeyakumar, V.; Mohebi, H.
2005
...and 62 more Documents
all top 5

#### Cited by 1,073 Authors

 120 Jeyakumar, Vaithilingam 48 Li, Guoyin 37 Yang, Xiaoqi 34 Lee, Gue Myung 32 Antczak, Tadeusz 29 Goberna, Miguel Angel 27 Mishra, Shashi Kant 23 Boţ, Radu Ioan 21 Wu, Zhiyou 20 Chuong, Thai Doan 20 López-Cerdá, Marco Antonio 20 Yao, Jen-Chih 19 Yang, Xinmin 17 Kuroiwa, Daishi 16 Wanka, Gert 15 Kim, Do Sang 15 Suzuki, Satoshi 15 Wang, Shouyang 15 Zalmai, G. J. 14 Sun, Xiangkai 13 Lee, Jae Hyoung 13 Soleimani-damaneh, Majid 13 Volle, Michel 12 Flores-Bazán, Fabián 12 Gadhi, Nazih Abderrazzak 12 Mohebi, Hossein 12 Nobakhtian, Soghra 12 Teo, Kok Lay 11 Dinh The Luc 11 Fang, Donghui 11 Ivanov, Vsevolod Ivanov 11 Jayswal, Anurag 11 Rubinov, Alexander M. 10 Ahmad, Izhar 10 Suneja, Surjeet Kaur 10 Nguyen Dong Yen 9 Craven, Bruce Desmond 9 Dinh, Ngo Van 9 Dinh, Nguyen Pham 9 Glover, Bevil Milton 9 Huy, Nguyen Quang 9 Li, Shengjie 9 Mehra, Aparna 8 Bhatia, Davinder 8 Chieu, Nguyen Huy 8 Do Van Luu 8 Pastor, Karel 8 Penot, Jean-Paul 8 Srisatkunarajah, Sivakolundu 8 Stancu-Minasian, Ioan M. 7 Bai, Fusheng 7 Chen, Jiawei 7 Dempe, Stephan 7 Ginchev, Ivan G. 7 Kassay, Gábor 7 Liu, Sanyang 7 Mordukhovich, Boris S. 7 Noor, Muhammad Aslam 7 Phan Quôc Khánh 7 Salahi, Maziar 7 Son, Ta Quang 6 Ansari, Qamrul Hasan 6 Chen, Zhe 6 Csetnek, Ernö Robert 6 Grad, Sorin-Mihai 6 Kohli, Bhawna 6 Long, Xianjun 6 Movahedian, Nooshin 6 Ng, Kung-Fu 6 Preda, Vasile C. 6 Rojas-Medar, Marko Antonio 6 Roshchina, Vera 6 Rufián-Lizana, Antonio 6 Sach, Pham Huu 6 Tuan, Nguyen Dinh 6 Verma, Ram U. 6 Vicente-Pérez, José 6 Zhao, Kequan 5 Bector, C. R. 5 Chen, Chunrong 5 Chen, Jein-Shan 5 Doagooei, Ali Reza 5 Guerraggio, Angelo 5 Gwinner, Joachim 5 Hodrea, Ioan Bogdan 5 Jiao, Liguo 5 Kostyukova, Olga Ivanova 5 Lai, Kuei-Kuei 5 Li, Duan 5 Li, Jun 5 Martínez-Legaz, Juan-Enrique 5 Mastroeni, Giandomenico 5 Mukherjee, Rathindra Nath 5 Novo-Sanjurjo, Vicente 5 Popovici, Nicolae 5 Quan, Jing 5 Rocca, Matteo 5 Schaible, Siegfried 5 Schöbel, Anita 5 Sisarat, Nithirat ...and 973 more Authors
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#### Cited in 139 Serials

 183 Journal of Optimization Theory and Applications 115 Optimization 98 Journal of Global Optimization 81 Journal of Mathematical Analysis and Applications 71 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 50 Optimization Letters 46 European Journal of Operational Research 39 Mathematical Programming. Series A. Series B 28 Numerical Functional Analysis and Optimization 25 SIAM Journal on Optimization 20 Journal of Inequalities and Applications 17 Operations Research Letters 16 Set-Valued and Variational Analysis 15 Applied Mathematics and Computation 14 Opsearch 14 Applied Mathematics Letters 14 Positivity 13 Computers & Mathematics with Applications 13 Top 12 Annals of Operations Research 10 Journal of Computational and Applied Mathematics 10 Journal of Industrial and Management Optimization 9 Computational Optimization and Applications 9 Mathematical Methods of Operations Research 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 6 Bulletin of the Australian Mathematical Society 6 Applied Mathematics and Optimization 6 Acta Mathematicae Applicatae Sinica. English Series 5 Asia-Pacific Journal of Operational Research 5 Mathematical and Computer Modelling 5 Linear Algebra and its Applications 5 Applied Mathematics. Series B (English Edition) 5 Vietnam Journal of Mathematics 5 Abstract and Applied Analysis 5 RAIRO. Operations Research 5 Journal of Systems Science and Complexity 4 Applicable Analysis 4 Fuzzy Sets and Systems 4 Journal of Approximation Theory 4 Rendiconti del Circolo Matemàtico di Palermo. Serie II 4 Applications of Mathematics 4 Journal of Applied Analysis 4 Fixed Point Theory and Applications 4 Journal of the Operations Research Society of China 3 Computer Methods in Applied Mechanics and Engineering 3 Kybernetika 3 International Journal of Computer Mathematics 3 Journal of Convex Analysis 3 Optimization Methods & Software 3 Taiwanese Journal of Mathematics 3 The ANZIAM Journal 3 Central European Journal of Mathematics 3 Journal of Nonlinear Analysis and Optimization: Theory & Applications 2 Archiv der Mathematik 2 Automatica 2 International Journal of Mathematics and Mathematical Sciences 2 Proceedings of the American Mathematical Society 2 ZOR. Zeitschrift für Operations Research 2 Journal of Mathematical Sciences (New York) 2 Computational and Applied Mathematics 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 Numerical Algebra, Control and Optimization 2 Mathematical Sciences 2 Open Mathematics 2 Journal of Nonlinear and Variational Analysis 1 International Journal of Control 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 1 Journal of Functional Analysis 1 Mathematics of Operations Research 1 Operations Research 1 SIAM Journal on Numerical Analysis 1 Siberian Mathematical Journal 1 Transactions of the American Mathematical Society 1 Insurance Mathematics & Economics 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Mathematica Hungarica 1 Neural Networks 1 Applied Mathematical Modelling 1 Pattern Recognition 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences ...and 39 more Serials
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#### Cited in 37 Fields

 1,043 Operations research, mathematical programming (90-XX) 455 Calculus of variations and optimal control; optimization (49-XX) 125 Real functions (26-XX) 71 Numerical analysis (65-XX) 48 Operator theory (47-XX) 47 Functional analysis (46-XX) 41 Convex and discrete geometry (52-XX) 25 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Global analysis, analysis on manifolds (58-XX) 17 Approximations and expansions (41-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 14 General topology (54-XX) 13 Computer science (68-XX) 8 Systems theory; control (93-XX) 7 Algebraic geometry (14-XX) 5 Mechanics of deformable solids (74-XX) 4 Statistics (62-XX) 3 Ordinary differential equations (34-XX) 3 Difference and functional equations (39-XX) 3 Probability theory and stochastic processes (60-XX) 3 Biology and other natural sciences (92-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Partial differential equations (35-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Differential geometry (53-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 Field theory and polynomials (12-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Mechanics of particles and systems (70-XX) 1 Information and communication theory, circuits (94-XX)

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