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## Gao, David Yang

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 Author ID: gao.david-yang Published as: Gao, David Yang; Gao, David Y.; Gao, David; Gao, D. Y.; Yang Gao, David; Gao, D. Yang
 Documents Indexed: 119 Publications since 1992, including 11 Books
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#### Co-Authors

 37 single-authored 13 Ruan, Ning 7 Fang, Shu-Cherng 5 Latorre, Vittorio 5 Ogden, Raymond William 5 Xing, Wenxun 5 Zhou, Xiaojun 5 Zhu, Jinghao 4 Feng, Zhaosheng 4 Sherali, Hanif D. 3 Ali, Elaf Jaafar 3 Chen, Yi 3 Sheu, Ruey-Lin 3 Wu, Changzhi 3 Yang, Chunhua 2 Cai, Kun 2 Hanoun, Samer 2 Jin, Zhong 2 Lu, Xiaojun 2 Nahavandi, Saeid 2 Qin, Qinghua 2 Wang, Zhenbo 1 Bhatti, Asim 1 Billups, Stephen C. 1 Debnath, Lokenath 1 Easterling, David R. 1 Fischer, Andreas M. 1 Floudas, Christodoulos Achilleus 1 Gao, Yan 1 Hajilarov, Eldar 1 Huang, Tingwen 1 Kelarev, Andrei Vladimirovich 1 Khan, Burhan 1 Li, Chaojie 1 Li, Chuandong 1 Li, Jie-Fang 1 Lin, Gang-Xuan 1 Liu, Guoshan 1 Liu, Jing 1 Machalová, Jitka 1 Motreanu, Dumitru 1 Neff, Patrizio 1 Netuka, Horymír 1 Roventa, Ionel 1 Sagratella, Simone 1 Singh, Vinai Kumar 1 Stavroulakis, Georgios E. 1 Tao, Shiming 1 Teo, Kok Lay 1 Thacker, William I. 1 Thiel, Christian 1 Viehland, D. 1 Wang, Shouyang 1 Wang, Xiaohui 1 Watson, Layne Terry 1 Wu, Dan 1 Wu, Soon-Yi 1 Xiao, Mingqing 1 Yang, Wei-Chi 1 Yearwood, J. L. 1 Yearwood, John 1 Yu, Haofeng 1 Zhang, Jiapu 1 Zheng, Shenzhou 1 Zhou, Jiani
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#### Serials

 14 Journal of Global Optimization 6 Journal of Industrial and Management Optimization 6 Advances in Mechanics and Mathematics 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Applied Mathematics and Computation 3 Journal of Computational and Applied Mathematics 2 IMA Journal of Applied Mathematics 2 Journal of Engineering Mathematics 2 Applied Mathematics and Optimization 2 Mechanics Research Communications 2 Studies in Applied Mathematics 2 Optimization 2 European Journal of Mechanics. A. Solids 2 Mathematics and Mechanics of Solids 2 Optimization and Engineering 2 Nonconvex Optimization and Its Applications 2 Optimization Letters 1 Bulletin of the Australian Mathematical Society 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal of Non-Linear Mechanics 1 International Journal of Solids and Structures 1 Journal of Mathematical Analysis and Applications 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Meccanica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Applied Mathematics and Mechanics. (English Edition) 1 International Journal of Computer Mathematics 1 Journal of Elasticity 1 Acta Mechanica Sinica. (English Edition) 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Continuum Mechanics and Thermodynamics 1 Computational Optimization and Applications 1 Nonlinear Dynamics 1 Optimization Methods & Software 1 Mathematical Methods of Operations Research 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Nonlinear Analysis. Real World Applications 1 Nonlinear Dynamics and Systems Theory 1 Communications in Mathematical Sciences 1 Fixed Point Theory and Applications 1 Numerical Algebra, Control and Optimization 1 Journal of Theoretical Biology 1 Springer Proceedings in Mathematics & Statistics 1 Mathematics and Mechanics of Complex Systems
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#### Fields

 66 Operations research, mathematical programming (90-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 47 Mechanics of deformable solids (74-XX) 12 Numerical analysis (65-XX) 11 General and overarching topics; collections (00-XX) 9 Partial differential equations (35-XX) 6 Ordinary differential equations (34-XX) 5 Operator theory (47-XX) 5 Mechanics of particles and systems (70-XX) 4 Systems theory; control (93-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Biology and other natural sciences (92-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH Open

89 Publications have been cited 647 times in 177 Documents Cited by Year
Duality principles in nonconvex systems. Theory, methods and applications. Zbl 0940.49001
Gao, David Yang
2000
Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. Zbl 0983.74053
Gao, David Yang
2000
Canonical duality theory and solutions to constrained nonconvex quadratic programming. Zbl 1075.90074
Gao, David Yang
2004
Solutions and optimality criteria to box constrained nonconvex minimization problems. Zbl 1171.90504
Gao, David Yang
2007
Perfect duality theory and complete solutions to a class of glocal optimization problems. Zbl 1040.49036
Gao, David Yang
2003
Nonlinear elastic beam theory with application in contact problems and variational approaches. Zbl 0843.73042
Gao, David Yang
1996
Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality. Zbl 1213.90258
Gao, David Yang; Ruan, Ning; Sherali, Hanif D.
2009
Analytic solutions and triality theory for nonconvex and nonsmooth variational problems with applications. Zbl 0983.49024
Gao, David Yang
2000
Global optimization for a class of fractional programming problems. Zbl 1206.90189
Fang, Shu-Cherng; Gao, David Y.; Sheu, Ruey-Lin; Xing, Wenxun
2009
Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem. Zbl 1143.74018
Gao, D. Y.; Ogden, R. W.
2008
Global extremal conditions for multi-integer quadratic programming. Zbl 1161.90457
Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun
2008
Finite deformation beam models and triality theory in dynamical post-buckling analysis. Zbl 1068.74569
Gao, David Yang
2000
Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation. Zbl 1153.74032
Gao, D. Y.; Ogden, R. W.
2008
Canonical dual approach to solving 0-1 quadratic programming problems. Zbl 1180.90195
Fang, Shu-Cherng; Gao, David Yang; Sheu, Ruey-Lin; Wu, Soon-Yi
2008
Duality, triality and complementary extremum principles in non-convex parametric variational problems with applications. Zbl 0923.49017
Gao, David Yang
1998
Multi-scale modelling and canonical dual finite element method in phase transitions of solids. Zbl 1169.74518
Gao, David Yang; Yu, Haofeng
2008
Solutions to quadratic minimization problems with box and integer constraints. Zbl 1222.90039
Gao, David Yang; Ruan, Ning
2010
Complete solutions and extremality criteria to polynomial optimization problems. Zbl 1104.90038
Gao, David Yang
2006
General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics. Zbl 0970.74011
Gao, David Yang
1999
Pure complementary energy principle and triality theory in finite elasticity. Zbl 0992.74013
Gao, David Yang
1999
Nonconvex semi-linear problems and canonical duality solutions. Zbl 1067.49024
Gao, David Yang
2003
Canonical duality theory: connections between nonconvex mechanics and global optimization. Zbl 1220.90159
Gao, David Y.; Sherali, Hanif D.
2009
Traveling wave solutions to a reaction-diffusion equation. Zbl 1176.35100
Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.
2009
Canonical duality for solving general nonconvex constrained problems. Zbl 1362.90315
Latorre, Vittorio; Gao, David Yang
2016
On the triality theory for a quartic polynomial optimization problem. Zbl 1364.90271
Gao, David Yang; Wu, Changzhi
2012
Complementarity, polarity and triality in non-smooth, non-convex and non-conservative Hamilton systems. Zbl 1097.49514
Gao, David Yang
2001
Canonical dual approach to solving the maximum cut problem. Zbl 1259.90154
Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun
2012
Optimization of matrix semirings for classification systems. Zbl 1244.16040
Gao, D. Y.; Kelarev, A. V.; Yearwood, J. L.
2011
Complementary finite-element method for finite deformation nonsmooth mechanics. Zbl 0857.73075
Gao, David Yang
1996
The Korteweg-de Vries-Burgers equation and its approximate solution. Zbl 1157.65057
Wang, Xiaohui; Feng, Zhaosheng; Debnath, Lokenath; Gao, David Y.
2008
Canonical duality theory. Unified methodology for multidisciplinary study. Zbl 1387.49002
Gao, David Yang (ed.); Latorre, Vittorio (ed.); Ruan, Ning (ed.)
2017
Mixed finite element solutions to contact problems of nonlinear Gao beam on elastic foundation. Zbl 1326.74075
Gao, D. Y.; Machalová, J.; Netuka, H.
2015
Canonical dual solutions for fixed cost quadratic programs. Zbl 1220.90072
Gao, David Yang; Ruan, Ning; Sherali, Hanif D.
2010
Global extremum criteria for finite elasticity. Zbl 0756.73035
Gao, David Yang
1992
A novel canonical dual computational approach for prion AGAAAAGA amyloid fibril molecular modeling. Zbl 1397.92548
Zhang, Jiapu; Gao, David Y.; Yearwood, John
2011
On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor. Zbl 1368.74013
Gao, David Yang; Neff, Patrizio; Roventa, Ionel; Thiel, Christian
2017
Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints. Zbl 1140.90506
Gao, David Yang
2005
Duality theory in nonlinear buckling analysis for von Kármán equations. Zbl 0832.73027
Gao, David Yang
1995
An extended beam theory for smart materials applications. II: Static formation problems. Zbl 0911.35039
Gao, D. Y.; Russell, D. L.
1998
Bi-complementarity and duality: A framework in nonlinear equilibria with applications to the contact problem of elastoplastic beam theory. Zbl 0971.74059
Gao, David Yang
1998
Applying the canonical dual theory in optimal control problems. Zbl 1258.49058
Zhu, Jinghao; Wu, Dan; Gao, David
2012
Canonical duality-triality theory: bridge between nonconvex analysis/mechanics and global optimization in complex system. Zbl 1382.49029
Gao, David Yang; Ruan, Ning; Latorre, Vittorio
2017
Analytic solutions to 3-D finite deformation problems governed by St Venant-Kirchhoff material. Zbl 1382.49056
Gao, David Yang; Hajilarov, Eldar
2017
A study on concave optimization via canonical dual function. Zbl 1279.90138
Zhu, Jinghao; Tao, Shiming; Gao, David
2009
Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem. Zbl 1145.90054
Gao, David Yang; Ruan, Ning
2008
Canonical dual least square method for solving general nonlinear systems of quadratic equations. Zbl 1200.90139
Ruan, N.; Gao, David Y.; Jiao, Y.
2010
Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions. Zbl 1369.90133
Chen, Yi; Gao, David Y.
2016
Global solutions to fractional programming problem with ratio of nonconvex functions. Zbl 1338.90403
Ruan, N.; Gao, D. Y.
2015
Minimal distance between two non-convex surfaces. Zbl 1152.90552
Gao, David Y.; Yang, Wei-Chi
2008
Multi-duality in minimal surface-type problems. Zbl 0833.49023
Gao, David Yang; Yang, Wei H.
1995
Complementary principle, algorithm, and complete solutions to phase transitions in solids governed by Landau-Ginzburg equation. Zbl 1081.74037
Gao, David Yang
2004
Canonical duality theory for topology optimization. Zbl 1382.49028
Gao, David Yang
2017
Improved canonical dual finite element method and algorithm for post-buckling analysis of nonlinear Gao beam. Zbl 1456.65151
Ali, Elaf Jaafar; Gao, David Yang
2017
On minimal distance between two surfaces. Zbl 1394.90452
Morales-Silva, Daniel; Gao, D. Y.
2017
Global optimal trajectory in chaos and NP-hardness. Zbl 1345.34024
Latorre, Vittorio; Gao, David Yang
2016
Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm. Zbl 1270.90041
Gao, David Yang; Watson, Layne T.; Easterling, David R.; Thacker, William I.; Billups, Stephen C.
2013
Canonical duality approach for non-linear dynamical systems. Zbl 1323.92185
Ruan, Ning; Gao, D. Y.
2014
Canonical duality theory and triality for solving general global optimization problems in complex systems. Zbl 1321.49055
Morales-Silva, Daniel; Gao, David
2015
Post-buckling solutions of hyper-elastic beam by canonical dual finite element method. Zbl 1298.74085
Cai, Kun; Gao, David Y.; Qin, Qing H.
2014
Double well potential function and its optimization in the $$N$$-dimensional real space. I. Zbl 1362.49015
Fang, Shu-Cherng; Gao, David Y.; Lin, Gang-Xuan; Sheu, Ruey-Lin; Xing, Wenxun
2017
Nonsmooth/ nonconvex mechanics. Modeling, analysis and numerical methods. A volume dedicated to the memory of Prof. P. D. Panagiotopoulos. Minisymposium within the ASME 1999 Mechanics and materials conference, Blacksburg, VA, USA, June 27–30, 1999. Zbl 0959.00041
Gao, David Y. (ed.); Ogden, Ray W. (ed.); Stavroulakis, Georgios (ed.)
2001
An extended beam theory for smart material applications. I: Extended beam models, duality theory, and finite element simulations. Zbl 0856.73026
Gao, D. Y.; Russell, D. L.
1996
On topology optimization and canonical duality method. Zbl 1440.74294
Gao, David Yang
2018
Analytic solutions to large deformation problems governed by generalized neo-Hookean model. Zbl 1382.49054
Gao, David Yang
2017
Triality theory for general unconstrained global optimization problems. Zbl 1382.49030
Gao, David Yang; Wu, Changzhi
2017
Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. Zbl 1382.49036
Ruan, Ning; Gao, David Yang
2017
Global solutions to spherically constrained quadratic minimization via canonical duality theory. Zbl 1382.49027
Chen, Yi; Gao, David Yang
2017
Global optimal solution to quadratic discrete programming problem with inequality constraints. Zbl 1382.49037
Ruan, Ning; Gao, David Yang
2017
On modeling and global solutions for d.c. optimization problems by canonical duality theory. Zbl 1411.90275
Jin, Zhong; Gao, David Y.
2017
On the extrema of a nonconvex functional with double-well potential in 1D. Zbl 1369.35021
Gao, David Yang; Lu, Xiaojun
2016
Analytical solutions to general anti-plane shear problems in finite elasticity. Zbl 1348.35265
Yang Gao, David
2016
Solution to nonconvex quadratic programming with both inequality and box constraints. Zbl 1178.90268
Zhang, Xi; Zhu, Jinghao; Gao, David Y.
2009
A nonconvex dissipative system and its applications. II. Zbl 1156.34005
Feng, Zhaosheng; Gao, David Y.
2008
Advances in applied mathematics and global optimization. In honor of Gilbert Strang on the occasion of his 70th birthday. Mainly selected lectures of the 1st international conference on complementarity, duality, and global optimization (CDGO), Blacksburg, VA, August 15–17, 2005. Zbl 1160.49001
Gao, David Y. (ed.); Sherali, Hanif D. (ed.)
2009
Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems. Zbl 1364.90280
Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua
2014
Tri-duality theory in phase transformations of ferroelectric crystals with random defects. Zbl 1183.74206
Gao, David Y.; Li, Jie-Fang; Viehland, D.
2004
Nonsmooth and nonconvex dynamics: Duality, polarity and complementary extremum principles. Zbl 0989.70016
Gao, David Yang
2001
Stability and extremum principles for post yield analysis of finite plasticity. Zbl 0874.73027
Gao, David Yang
1994
Global optimization by canonical dual function. Zbl 1223.90049
Zhu, Jinghao; Zhou, Jiani; Gao, David
2010
On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications. Zbl 1462.90099
Ruan, Ning; Gao, David Yang
2018
Remarks on analytic solutions and ellipticity in anti-plane shear problems of nonlinear elasticity. Zbl 1382.49055
Gao, David Yang
2017
Canonical duality method for solving Kantorovich mass transfer problem. Zbl 1382.49035
Lu, Xiaojun; Gao, David Yang
2017
Canonical duality theory for solving non-monotone variational inequality problems. Zbl 1382.49034
Liu, Guoshan; Gao, David Yang; Wang, Shouyang
2017
On d.c. optimization problems. Zbl 1382.49031
Jin, Zhong; Gao, David Yang
2017
On SDP method for solving canonical dual problem in post buckling of large deformed elastic beam. Zbl 1460.74027
Ali, Elaf Jaafar; Gao, David Yang
2018
Canonical duality for solving nonconvex and nonsmooth optimization problem. Zbl 1171.65048
Liu, Jing; Gao, David Y.; Gao, Yan
2009
Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in $$\mathbb{R}^n$$. Zbl 1264.90143
Morales-Silva, Daniel; Gao, David Yang
2013
Postbuckling analysis of a nonlinear beam with axial functionally graded material. Zbl 1359.74395
Cai, Kun; Gao, David Y.; Qin, Qing H.
2014
Global solutions to a class of CEC benchmark constrained optimization problems. Zbl 1345.90072
Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua
2016
On topology optimization and canonical duality method. Zbl 1440.74294
Gao, David Yang
2018
On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications. Zbl 1462.90099
Ruan, Ning; Gao, David Yang
2018
On SDP method for solving canonical dual problem in post buckling of large deformed elastic beam. Zbl 1460.74027
Ali, Elaf Jaafar; Gao, David Yang
2018
Canonical duality theory. Unified methodology for multidisciplinary study. Zbl 1387.49002
Gao, David Yang; Latorre, Vittorio; Ruan, Ning
2017
On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor. Zbl 1368.74013
Gao, David Yang; Neff, Patrizio; Roventa, Ionel; Thiel, Christian
2017
Canonical duality-triality theory: bridge between nonconvex analysis/mechanics and global optimization in complex system. Zbl 1382.49029
Gao, David Yang; Ruan, Ning; Latorre, Vittorio
2017
Analytic solutions to 3-D finite deformation problems governed by St Venant-Kirchhoff material. Zbl 1382.49056
Gao, David Yang; Hajilarov, Eldar
2017
Canonical duality theory for topology optimization. Zbl 1382.49028
Gao, David Yang
2017
Improved canonical dual finite element method and algorithm for post-buckling analysis of nonlinear Gao beam. Zbl 1456.65151
Ali, Elaf Jaafar; Gao, David Yang
2017
On minimal distance between two surfaces. Zbl 1394.90452
Morales-Silva, Daniel; Gao, D. Y.
2017
Double well potential function and its optimization in the $$N$$-dimensional real space. I. Zbl 1362.49015
Fang, Shu-Cherng; Gao, David Y.; Lin, Gang-Xuan; Sheu, Ruey-Lin; Xing, Wenxun
2017
Analytic solutions to large deformation problems governed by generalized neo-Hookean model. Zbl 1382.49054
Gao, David Yang
2017
Triality theory for general unconstrained global optimization problems. Zbl 1382.49030
Gao, David Yang; Wu, Changzhi
2017
Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. Zbl 1382.49036
Ruan, Ning; Gao, David Yang
2017
Global solutions to spherically constrained quadratic minimization via canonical duality theory. Zbl 1382.49027
Chen, Yi; Gao, David Yang
2017
Global optimal solution to quadratic discrete programming problem with inequality constraints. Zbl 1382.49037
Ruan, Ning; Gao, David Yang
2017
On modeling and global solutions for d.c. optimization problems by canonical duality theory. Zbl 1411.90275
Jin, Zhong; Gao, David Y.
2017
Remarks on analytic solutions and ellipticity in anti-plane shear problems of nonlinear elasticity. Zbl 1382.49055
Gao, David Yang
2017
Canonical duality method for solving Kantorovich mass transfer problem. Zbl 1382.49035
Lu, Xiaojun; Gao, David Yang
2017
Canonical duality theory for solving non-monotone variational inequality problems. Zbl 1382.49034
Liu, Guoshan; Gao, David Yang; Wang, Shouyang
2017
On d.c. optimization problems. Zbl 1382.49031
Jin, Zhong; Gao, David Yang
2017
Canonical duality for solving general nonconvex constrained problems. Zbl 1362.90315
Latorre, Vittorio; Gao, David Yang
2016
Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions. Zbl 1369.90133
Chen, Yi; Gao, David Y.
2016
Global optimal trajectory in chaos and NP-hardness. Zbl 1345.34024
Latorre, Vittorio; Gao, David Yang
2016
On the extrema of a nonconvex functional with double-well potential in 1D. Zbl 1369.35021
Gao, David Yang; Lu, Xiaojun
2016
Analytical solutions to general anti-plane shear problems in finite elasticity. Zbl 1348.35265
Yang Gao, David
2016
Global solutions to a class of CEC benchmark constrained optimization problems. Zbl 1345.90072
Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua
2016
Mixed finite element solutions to contact problems of nonlinear Gao beam on elastic foundation. Zbl 1326.74075
Gao, D. Y.; Machalová, J.; Netuka, H.
2015
Global solutions to fractional programming problem with ratio of nonconvex functions. Zbl 1338.90403
Ruan, N.; Gao, D. Y.
2015
Canonical duality theory and triality for solving general global optimization problems in complex systems. Zbl 1321.49055
Morales-Silva, Daniel; Gao, David
2015
Canonical duality approach for non-linear dynamical systems. Zbl 1323.92185
Ruan, Ning; Gao, D. Y.
2014
Post-buckling solutions of hyper-elastic beam by canonical dual finite element method. Zbl 1298.74085
Cai, Kun; Gao, David Y.; Qin, Qing H.
2014
Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems. Zbl 1364.90280
Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua
2014
Postbuckling analysis of a nonlinear beam with axial functionally graded material. Zbl 1359.74395
Cai, Kun; Gao, David Y.; Qin, Qing H.
2014
Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm. Zbl 1270.90041
Gao, David Yang; Watson, Layne T.; Easterling, David R.; Thacker, William I.; Billups, Stephen C.
2013
Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in $$\mathbb{R}^n$$. Zbl 1264.90143
Morales-Silva, Daniel; Gao, David Yang
2013
On the triality theory for a quartic polynomial optimization problem. Zbl 1364.90271
Gao, David Yang; Wu, Changzhi
2012
Canonical dual approach to solving the maximum cut problem. Zbl 1259.90154
Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun
2012
Applying the canonical dual theory in optimal control problems. Zbl 1258.49058
Zhu, Jinghao; Wu, Dan; Gao, David
2012
Optimization of matrix semirings for classification systems. Zbl 1244.16040
Gao, D. Y.; Kelarev, A. V.; Yearwood, J. L.
2011
A novel canonical dual computational approach for prion AGAAAAGA amyloid fibril molecular modeling. Zbl 1397.92548
Zhang, Jiapu; Gao, David Y.; Yearwood, John
2011
Solutions to quadratic minimization problems with box and integer constraints. Zbl 1222.90039
Gao, David Yang; Ruan, Ning
2010
Canonical dual solutions for fixed cost quadratic programs. Zbl 1220.90072
Gao, David Yang; Ruan, Ning; Sherali, Hanif D.
2010
Canonical dual least square method for solving general nonlinear systems of quadratic equations. Zbl 1200.90139
Ruan, N.; Gao, David Y.; Jiao, Y.
2010
Global optimization by canonical dual function. Zbl 1223.90049
Zhu, Jinghao; Zhou, Jiani; Gao, David
2010
Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality. Zbl 1213.90258
Gao, David Yang; Ruan, Ning; Sherali, Hanif D.
2009
Global optimization for a class of fractional programming problems. Zbl 1206.90189
Fang, Shu-Cherng; Gao, David Y.; Sheu, Ruey-Lin; Xing, Wenxun
2009
Canonical duality theory: connections between nonconvex mechanics and global optimization. Zbl 1220.90159
Gao, David Y.; Sherali, Hanif D.
2009
Traveling wave solutions to a reaction-diffusion equation. Zbl 1176.35100
Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.
2009
A study on concave optimization via canonical dual function. Zbl 1279.90138
Zhu, Jinghao; Tao, Shiming; Gao, David
2009
Solution to nonconvex quadratic programming with both inequality and box constraints. Zbl 1178.90268
Zhang, Xi; Zhu, Jinghao; Gao, David Y.
2009
Advances in applied mathematics and global optimization. In honor of Gilbert Strang on the occasion of his 70th birthday. Mainly selected lectures of the 1st international conference on complementarity, duality, and global optimization (CDGO), Blacksburg, VA, August 15–17, 2005. Zbl 1160.49001
Gao, David Y.; Sherali, Hanif D.
2009
Canonical duality for solving nonconvex and nonsmooth optimization problem. Zbl 1171.65048
Liu, Jing; Gao, David Y.; Gao, Yan
2009
Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem. Zbl 1143.74018
Gao, D. Y.; Ogden, R. W.
2008
Global extremal conditions for multi-integer quadratic programming. Zbl 1161.90457
Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun
2008
Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation. Zbl 1153.74032
Gao, D. Y.; Ogden, R. W.
2008
Canonical dual approach to solving 0-1 quadratic programming problems. Zbl 1180.90195
Fang, Shu-Cherng; Gao, David Yang; Sheu, Ruey-Lin; Wu, Soon-Yi
2008
Multi-scale modelling and canonical dual finite element method in phase transitions of solids. Zbl 1169.74518
Gao, David Yang; Yu, Haofeng
2008
The Korteweg-de Vries-Burgers equation and its approximate solution. Zbl 1157.65057
Wang, Xiaohui; Feng, Zhaosheng; Debnath, Lokenath; Gao, David Y.
2008
Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem. Zbl 1145.90054
Gao, David Yang; Ruan, Ning
2008
Minimal distance between two non-convex surfaces. Zbl 1152.90552
Gao, David Y.; Yang, Wei-Chi
2008
A nonconvex dissipative system and its applications. II. Zbl 1156.34005
Feng, Zhaosheng; Gao, David Y.
2008
Solutions and optimality criteria to box constrained nonconvex minimization problems. Zbl 1171.90504
Gao, David Yang
2007
Complete solutions and extremality criteria to polynomial optimization problems. Zbl 1104.90038
Gao, David Yang
2006
Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints. Zbl 1140.90506
Gao, David Yang
2005
Canonical duality theory and solutions to constrained nonconvex quadratic programming. Zbl 1075.90074
Gao, David Yang
2004
Complementary principle, algorithm, and complete solutions to phase transitions in solids governed by Landau-Ginzburg equation. Zbl 1081.74037
Gao, David Yang
2004
Tri-duality theory in phase transformations of ferroelectric crystals with random defects. Zbl 1183.74206
Gao, David Y.; Li, Jie-Fang; Viehland, D.
2004
Perfect duality theory and complete solutions to a class of glocal optimization problems. Zbl 1040.49036
Gao, David Yang
2003
Nonconvex semi-linear problems and canonical duality solutions. Zbl 1067.49024
Gao, David Yang
2003
Complementarity, polarity and triality in non-smooth, non-convex and non-conservative Hamilton systems. Zbl 1097.49514
Gao, David Yang
2001
Nonsmooth/ nonconvex mechanics. Modeling, analysis and numerical methods. A volume dedicated to the memory of Prof. P. D. Panagiotopoulos. Minisymposium within the ASME 1999 Mechanics and materials conference, Blacksburg, VA, USA, June 27–30, 1999. Zbl 0959.00041
Gao, David Y.; Ogden, Ray W.; Stavroulakis, Georgios
2001
Nonsmooth and nonconvex dynamics: Duality, polarity and complementary extremum principles. Zbl 0989.70016
Gao, David Yang
2001
Duality principles in nonconvex systems. Theory, methods and applications. Zbl 0940.49001
Gao, David Yang
2000
Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. Zbl 0983.74053
Gao, David Yang
2000
Analytic solutions and triality theory for nonconvex and nonsmooth variational problems with applications. Zbl 0983.49024
Gao, David Yang
2000
Finite deformation beam models and triality theory in dynamical post-buckling analysis. Zbl 1068.74569
Gao, David Yang
2000
General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics. Zbl 0970.74011
Gao, David Yang
1999
Pure complementary energy principle and triality theory in finite elasticity. Zbl 0992.74013
Gao, David Yang
1999
Duality, triality and complementary extremum principles in non-convex parametric variational problems with applications. Zbl 0923.49017
Gao, David Yang
1998
An extended beam theory for smart materials applications. II: Static formation problems. Zbl 0911.35039
Gao, D. Y.; Russell, D. L.
1998
Bi-complementarity and duality: A framework in nonlinear equilibria with applications to the contact problem of elastoplastic beam theory. Zbl 0971.74059
Gao, David Yang
1998
Nonlinear elastic beam theory with application in contact problems and variational approaches. Zbl 0843.73042
Gao, David Yang
1996
Complementary finite-element method for finite deformation nonsmooth mechanics. Zbl 0857.73075
Gao, David Yang
1996
An extended beam theory for smart material applications. I: Extended beam models, duality theory, and finite element simulations. Zbl 0856.73026
Gao, D. Y.; Russell, D. L.
1996
Duality theory in nonlinear buckling analysis for von Kármán equations. Zbl 0832.73027
Gao, David Yang
1995
Multi-duality in minimal surface-type problems. Zbl 0833.49023
Gao, David Yang; Yang, Wei H.
1995
Stability and extremum principles for post yield analysis of finite plasticity. Zbl 0874.73027
Gao, David Yang
1994
Global extremum criteria for finite elasticity. Zbl 0756.73035
Gao, David Yang
1992
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#### Cited by 233 Authors

 43 Gao, David Yang 11 Zhu, Jinghao 10 Zălinescu, Constantin 9 Fang, Shu-Cherng 7 Xing, Wenxun 6 Sheu, Ruey-Lin 5 Ruan, Ning 5 Xia, Yong 4 Ahn, Jeongho 4 Feng, Zhaosheng 4 Machalová, Jitka 4 Netuka, Horymír 4 Shillor, Meir 4 Voisei, Mircea Dan 3 Cai, Kun 3 Jiao, Hongwei 3 Latorre, Vittorio 3 Li, Duan 3 Merodio, Jose 3 Spector, Scott J. 3 Zhou, Jiani 3 Zhou, Xiaojun 2 Ali, Elaf Jaafar 2 Aslan, İsmail 2 Bajer, Czesław I. 2 Birgin, Ernesto G. 2 Dyniewicz, Bartłomiej 2 Easterling, David R. 2 El Hamdaoui, Mustapha 2 Floudas, Christodoulos Achilleus 2 Gao, Yan 2 Li, Chaojie 2 Lin, Gang-Xuan 2 Liu, Guohua 2 Liu, Jing 2 Liu, Sanyang 2 Lu, Xiaojun 2 Martínez, José Mario 2 M’Bengue, M’Bagne F. 2 Neff, Patrizio 2 Ogden, Raymond William 2 Park, Eun-Jae 2 Qin, Qinghua 2 Ray, Sumita Saha 2 Saad, Khaled Mohammed 2 Sahoo, Subhadarshan 2 Spector, Daniel E. 2 Sun, Xiaoling 2 Wang, Zhenbo 2 Watson, Layne Terry 2 Wu, Changzhi 2 Wu, Dan 2 Xu, Yifan 2 Yang, Chunhua 2 Zhao, Shangrui 2 Zheng, Xiaojin 1 Al-Sharif, Eman Hussain Faissal 1 Almeida, J. P. M. 1 Andrews, Kevin T. 1 Andrica, Dorin 1 Arana-Jiménez, Manuel 1 Arqub, Omar Abu 1 Atangana, Abdon 1 Baaser, Herbert 1 Baek, Seungik 1 Bai, Yanqin 1 Băleanu, Dumitru I. 1 Billups, Stephen C. 1 Borrero, Juan S. 1 Bouchitté, Guy 1 Brigadnov, Igor A. 1 Cai, Hongyan 1 Cambini, Riccardo 1 Carosi, Laura 1 Castle, Brent S. 1 Chen, Hui-Mei 1 Chen, Qiuhui 1 Chen, Yi 1 Chen, Yongqiang 1 Cheng, Gengdong 1 Colmegna, P. 1 Dagher, M. A. 1 Dai, Ning 1 Davini, Cesare 1 Deng, Zhibin 1 Desai, Jitamitra 1 DiPillo, Gianni 1 Du, Shouqiang 1 Dumont, Yves 1 El-Ajou, Ahmad 1 El-Ganaini, Shoukry Ibrahim Atia 1 Fan, Bin 1 Fearing, Ron S. 1 Feng, Joe-Mei 1 Fessel, Kimberly 1 Fragalà, Ilaria 1 Gao, Yuchen 1 Gao, Zheming 1 Ge, JuHong 1 Ghorbanpour Arani, Ali ...and 133 more Authors
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#### Cited in 64 Serials

 28 Journal of Global Optimization 9 Applied Mathematics and Computation 8 Mathematics and Mechanics of Solids 8 Optimization Letters 7 Journal of Engineering Mathematics 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Journal of Industrial and Management Optimization 4 Journal of Computational and Applied Mathematics 4 Optimization 4 Journal of Elasticity 4 Computational Optimization and Applications 4 Optimization and Engineering 3 Acta Mechanica 3 Journal of Optimization Theory and Applications 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 European Journal of Operational Research 3 Optimization Methods & Software 3 Mathematical Methods of Operations Research 3 Nonlinear Analysis. Real World Applications 2 Archive for Rational Mechanics and Analysis 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal of Solids and Structures 2 Mathematical Methods in the Applied Sciences 2 Discrete and Continuous Dynamical Systems 2 Mathematical Problems in Engineering 2 European Journal of Control 2 Nonlinear Dynamics 2 Journal of Combinatorial Optimization 2 Journal of Applied Mathematics 2 Mathematical Biosciences and Engineering 2 Journal of Control Science and Engineering 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 International Journal of Control 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Wave Motion 1 Chaos, Solitons and Fractals 1 Studies in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Computational Mechanics 1 Numerical Methods for Partial Differential Equations 1 Asia-Pacific Journal of Operational Research 1 Neural Networks 1 Annals of Operations Research 1 Applied Mathematical Modelling 1 Acta Mechanica Sinica. (English Edition) 1 Mathematical Programming. Series A. Series B 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Continuum Mechanics and Thermodynamics 1 Computational and Applied Mathematics 1 INFORMS Journal on Computing 1 Abstract and Applied Analysis 1 Chaos 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Communications in Nonlinear Science and Numerical Simulation 1 Mediterranean Journal of Mathematics 1 Fixed Point Theory and Applications 1 Advances in Difference Equations 1 Science in China. Series G 1 Discrete and Continuous Dynamical Systems. Series S 1 Advances in Mathematical Physics 1 Science China. Mathematics
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#### Cited in 26 Fields

 90 Operations research, mathematical programming (90-XX) 55 Mechanics of deformable solids (74-XX) 34 Partial differential equations (35-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 22 Numerical analysis (65-XX) 6 Ordinary differential equations (34-XX) 6 Systems theory; control (93-XX) 4 Real functions (26-XX) 4 Fluid mechanics (76-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Operator theory (47-XX) 3 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)