Edit Profile (opens in new tab) Gao, David Yang Compute Distance To: Compute Author ID: gao.david-yang Published as: Gao, David Yang; Gao, David Y.; Gao, David; Gao, D. Y.; Yang Gao, David more...less Documents Indexed: 110 Publications since 1992, including 3 Books 9 Contributions as Editor Co-Authors: 60 Co-Authors with 72 Joint Publications 2,772 Co-Co-Authors all top 5 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 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, Chao 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 all top 5 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 all top 5 Fields 67 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 90 Publications have been cited 673 times in 201 Documents Cited by ▼ Year ▼ Duality principles in nonconvex systems. Theory, methods and applications. Zbl 0940.49001Gao, David Yang 44 2000 Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. Zbl 0983.74053Gao, David Yang 36 2000 Canonical duality theory and solutions to constrained nonconvex quadratic programming. Zbl 1075.90074Gao, David Yang 36 2004 Solutions and optimality criteria to box constrained nonconvex minimization problems. Zbl 1171.90504Gao, David Yang 30 2007 Perfect duality theory and complete solutions to a class of glocal optimization problems. Zbl 1040.49036Gao, David Yang 28 2003 Nonlinear elastic beam theory with application in contact problems and variational approaches. Zbl 0843.73042Gao, David Yang 26 1996 Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality. Zbl 1213.90258Gao, David Yang; Ruan, Ning; Sherali, Hanif D. 24 2009 Global optimization for a class of fractional programming problems. Zbl 1206.90189Fang, Shu-Cherng; Gao, David Y.; Sheu, Ruey-Lin; Xing, Wenxun 20 2009 Finite deformation beam models and triality theory in dynamical post-buckling analysis. Zbl 1068.74569Gao, David Yang 20 2000 Analytic solutions and triality theory for nonconvex and nonsmooth variational problems with applications. Zbl 0983.49024Gao, David Yang 19 2000 Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem. Zbl 1143.74018Gao, D. Y.; Ogden, R. W. 17 2008 Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation. Zbl 1153.74032Gao, D. Y.; Ogden, R. W. 17 2008 Global extremal conditions for multi-integer quadratic programming. Zbl 1161.90457Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun 17 2008 Canonical dual approach to solving 0-1 quadratic programming problems. Zbl 1180.90195Fang, Shu-Cherng; Gao, David Yang; Sheu, Ruey-Lin; Wu, Soon-Yi 16 2008 Multi-scale modelling and canonical dual finite element method in phase transitions of solids. Zbl 1169.74518Gao, David Yang; Yu, Haofeng 15 2008 Duality, triality and complementary extremum principles in non-convex parametric variational problems with applications. Zbl 0923.49017Gao, David Yang 14 1998 Solutions to quadratic minimization problems with box and integer constraints. Zbl 1222.90039Gao, David Yang; Ruan, Ning 13 2010 Nonconvex semi-linear problems and canonical duality solutions. Zbl 1067.49024Gao, David Yang 12 2003 Complete solutions and extremality criteria to polynomial optimization problems. Zbl 1104.90038Gao, David Yang 12 2006 General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics. Zbl 0970.74011Gao, David Yang 12 1999 Pure complementary energy principle and triality theory in finite elasticity. Zbl 0992.74013Gao, David Yang 12 1999 Canonical duality for solving general nonconvex constrained problems. Zbl 1362.90315Latorre, Vittorio; Gao, David Yang 12 2016 Traveling wave solutions to a reaction-diffusion equation. Zbl 1176.35100Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y. 11 2009 Canonical duality theory: connections between nonconvex mechanics and global optimization. Zbl 1220.90159Gao, David Y.; Sherali, Hanif D. 11 2009 On the triality theory for a quartic polynomial optimization problem. Zbl 1364.90271Gao, David Yang; Wu, Changzhi 10 2012 Mixed finite element solutions to contact problems of nonlinear Gao beam on elastic foundation. Zbl 1326.74075Gao, D. Y.; Machalová, J.; Netuka, H. 9 2015 Complementarity, polarity and triality in non-smooth, non-convex and non-conservative Hamilton systems. Zbl 1097.49514Gao, David Yang 9 2001 Canonical duality theory. Unified methodology for multidisciplinary study. Zbl 1387.49002 9 2017 Optimization of matrix semirings for classification systems. Zbl 1244.16040Gao, D. Y.; Kelarev, A. V.; Yearwood, J. L. 8 2011 Canonical dual approach to solving the maximum cut problem. Zbl 1259.90154Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun 8 2012 Complementary finite-element method for finite deformation nonsmooth mechanics. Zbl 0857.73075Gao, David Yang 7 1996 Canonical dual solutions for fixed cost quadratic programs. Zbl 1220.90072Gao, David Yang; Ruan, Ning; Sherali, Hanif D. 6 2010 Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem. Zbl 1145.90054Gao, David Yang; Ruan, Ning 6 2008 The Korteweg-de Vries-Burgers equation and its approximate solution. Zbl 1157.65057Wang, Xiaohui; Feng, Zhaosheng; Debnath, Lokenath; Gao, David Y. 6 2008 On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor. Zbl 1368.74013Gao, David Yang; Neff, Patrizio; Roventa, Ionel; Thiel, Christian 6 2017 Global extremum criteria for finite elasticity. Zbl 0756.73035Gao, David Yang 5 1992 Bi-complementarity and duality: A framework in nonlinear equilibria with applications to the contact problem of elastoplastic beam theory. Zbl 0971.74059Gao, David Yang 5 1998 On topology optimization and canonical duality method. Zbl 1440.74294Gao, David Yang 5 2018 A novel canonical dual computational approach for prion AGAAAAGA amyloid fibril molecular modeling. Zbl 1397.92548Zhang, Jiapu; Gao, David Y.; Yearwood, John 5 2011 Double well potential function and its optimization in the \(N\)-dimensional real space. I. Zbl 1362.49015Fang, Shu-Cherng; Gao, David Y.; Lin, Gang-Xuan; Sheu, Ruey-Lin; Xing, Wenxun 5 2017 Canonical duality-triality theory: bridge between nonconvex analysis/mechanics and global optimization in complex system. Zbl 1382.49029Gao, David Yang; Ruan, Ning; Latorre, Vittorio 5 2017 A study on concave optimization via canonical dual function. Zbl 1279.90138Zhu, Jinghao; Tao, Shiming; Gao, David 4 2009 Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints. Zbl 1140.90506Gao, David Yang 4 2005 Minimal distance between two non-convex surfaces. Zbl 1152.90552Gao, David Y.; Yang, Wei-Chi 4 2008 An extended beam theory for smart materials applications. II: Static formation problems. Zbl 0911.35039Gao, D. Y.; Russell, D. L. 4 1998 Canonical dual least square method for solving general nonlinear systems of quadratic equations. Zbl 1200.90139Ruan, N.; Gao, David Y.; Jiao, Y. 4 2010 Applying the canonical dual theory in optimal control problems. Zbl 1258.49058Zhu, Jinghao; Wu, Dan; Gao, David 4 2012 Duality theory in nonlinear buckling analysis for von Kármán equations. Zbl 0832.73027Gao, David Yang 4 1995 Global solutions to fractional programming problem with ratio of nonconvex functions. Zbl 1338.90403Ruan, N.; Gao, D. Y. 4 2015 Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions. Zbl 1369.90133Chen, Yi; Gao, David Y. 4 2016 Analytic solutions to 3-D finite deformation problems governed by St Venant-Kirchhoff material. Zbl 1382.49056Gao, David Yang; Hajilarov, Eldar 4 2017 On minimal distance between two surfaces. Zbl 1394.90452Morales-Silva, Daniel; Gao, D. Y. 4 2017 Complementary principle, algorithm, and complete solutions to phase transitions in solids governed by Landau-Ginzburg equation. Zbl 1081.74037Gao, David Yang 3 2004 Post-buckling solutions of hyper-elastic beam by canonical dual finite element method. Zbl 1298.74085Cai, Kun; Gao, David Y.; Qin, Qing H. 3 2014 Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm. Zbl 1270.90041Gao, David Yang; Watson, Layne T.; Easterling, David R.; Thacker, William I.; Billups, Stephen C. 3 2013 Multi-duality in minimal surface-type problems. Zbl 0833.49023Gao, David Yang; Yang, Wei H. 3 1995 On the extrema of a nonconvex functional with double-well potential in 1D. Zbl 1369.35021Gao, David Yang; Lu, Xiaojun 3 2016 Global optimal trajectory in chaos and NP-hardness. Zbl 1345.34024Latorre, Vittorio; Gao, David Yang 3 2016 Analytical solutions to general anti-plane shear problems in finite elasticity. Zbl 1348.35265Yang Gao, David 3 2016 Triality theory for general unconstrained global optimization problems. Zbl 1382.49030Gao, David Yang; Wu, Changzhi 3 2017 Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. Zbl 1382.49036Ruan, Ning; Gao, David Yang 3 2017 Canonical duality theory for topology optimization. Zbl 1382.49028Gao, David Yang 3 2017 Improved canonical dual finite element method and algorithm for post-buckling analysis of nonlinear Gao beam. Zbl 1456.65151Ali, Elaf Jaafar; Gao, David Yang 3 2017 Global optimal solution to quadratic discrete programming problem with inequality constraints. Zbl 1382.49037Ruan, Ning; Gao, David Yang 3 2017 Solution to nonconvex quadratic programming with both inequality and box constraints. Zbl 1178.90268Zhang, Xi; Zhu, Jinghao; Gao, David Y. 2 2009 Canonical duality theory and triality for solving general global optimization problems in complex systems. Zbl 1321.49055Morales-Silva, Daniel; Gao, David 2 2015 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 2 2009 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 2 2001 On modeling and global solutions for d.c. optimization problems by canonical duality theory. Zbl 1411.90275Jin, Zhong; Gao, David Y. 2 2017 Canonical duality approach for non-linear dynamical systems. Zbl 1323.92185Ruan, Ning; Gao, D. Y. 2 2014 An extended beam theory for smart material applications. I: Extended beam models, duality theory, and finite element simulations. Zbl 0856.73026Gao, D. Y.; Russell, D. L. 2 1996 On SDP method for solving canonical dual problem in post buckling of large deformed elastic beam. Zbl 1460.74027Ali, Elaf Jaafar; Gao, David Yang 2 2018 Analytic solutions to large deformation problems governed by generalized neo-Hookean model. Zbl 1382.49054Gao, David Yang 2 2017 Global solutions to spherically constrained quadratic minimization via canonical duality theory. Zbl 1382.49027Chen, Yi; Gao, David Yang 2 2017 Tri-duality theory in phase transformations of ferroelectric crystals with random defects. Zbl 1183.74206Gao, David Y.; Li, Jie-Fang; Viehland, D. 1 2004 Canonical duality for solving nonconvex and nonsmooth optimization problem. Zbl 1171.65048Liu, Jing; Gao, David Y.; Gao, Yan 1 2009 Nonsmooth and nonconvex dynamics: Duality, polarity and complementary extremum principles. Zbl 0989.70016Gao, David Yang 1 2001 Duality in distributed-parameter control of nonconvex and nonconservative dynamical systems with applications. Zbl 1112.49033Gao, David Yang 1 2006 A nonconvex dissipative system and its applications. II. Zbl 1156.34005Feng, Zhaosheng; Gao, David Y. 1 2008 Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in \(\mathbb{R}^n \). Zbl 1264.90143Morales-Silva, Daniel; Gao, David Yang 1 2013 Global optimization by canonical dual function. Zbl 1223.90049Zhu, Jinghao; Zhou, Jiani; Gao, David 1 2010 Stability and extremum principles for post yield analysis of finite plasticity. Zbl 0874.73027Gao, David Yang 1 1994 Global solutions to a class of CEC benchmark constrained optimization problems. Zbl 1345.90072Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua 1 2016 Postbuckling analysis of a nonlinear beam with axial functionally graded material. Zbl 1359.74395Cai, Kun; Gao, David Y.; Qin, Qing H. 1 2014 On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications. Zbl 1462.90099Ruan, Ning; Gao, David Yang 1 2018 Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems. Zbl 1364.90280Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua 1 2014 Remarks on analytic solutions and ellipticity in anti-plane shear problems of nonlinear elasticity. Zbl 1382.49055Gao, David Yang 1 2017 Canonical duality method for solving Kantorovich mass transfer problem. Zbl 1382.49035Lu, Xiaojun; Gao, David Yang 1 2017 Canonical duality theory for solving non-monotone variational inequality problems. Zbl 1382.49034Liu, Guoshan; Gao, David Yang; Wang, Shouyang 1 2017 On d.c. optimization problems. Zbl 1382.49031Jin, Zhong; Gao, David Yang 1 2017 On topology optimization and canonical duality method. Zbl 1440.74294Gao, David Yang 5 2018 On SDP method for solving canonical dual problem in post buckling of large deformed elastic beam. Zbl 1460.74027Ali, Elaf Jaafar; Gao, David Yang 2 2018 On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications. Zbl 1462.90099Ruan, Ning; Gao, David Yang 1 2018 Canonical duality theory. Unified methodology for multidisciplinary study. Zbl 1387.49002 9 2017 On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor. Zbl 1368.74013Gao, David Yang; Neff, Patrizio; Roventa, Ionel; Thiel, Christian 6 2017 Double well potential function and its optimization in the \(N\)-dimensional real space. I. Zbl 1362.49015Fang, Shu-Cherng; Gao, David Y.; Lin, Gang-Xuan; Sheu, Ruey-Lin; Xing, Wenxun 5 2017 Canonical duality-triality theory: bridge between nonconvex analysis/mechanics and global optimization in complex system. Zbl 1382.49029Gao, David Yang; Ruan, Ning; Latorre, Vittorio 5 2017 Analytic solutions to 3-D finite deformation problems governed by St Venant-Kirchhoff material. Zbl 1382.49056Gao, David Yang; Hajilarov, Eldar 4 2017 On minimal distance between two surfaces. Zbl 1394.90452Morales-Silva, Daniel; Gao, D. Y. 4 2017 Triality theory for general unconstrained global optimization problems. Zbl 1382.49030Gao, David Yang; Wu, Changzhi 3 2017 Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. Zbl 1382.49036Ruan, Ning; Gao, David Yang 3 2017 Canonical duality theory for topology optimization. Zbl 1382.49028Gao, David Yang 3 2017 Improved canonical dual finite element method and algorithm for post-buckling analysis of nonlinear Gao beam. Zbl 1456.65151Ali, Elaf Jaafar; Gao, David Yang 3 2017 Global optimal solution to quadratic discrete programming problem with inequality constraints. Zbl 1382.49037Ruan, Ning; Gao, David Yang 3 2017 On modeling and global solutions for d.c. optimization problems by canonical duality theory. Zbl 1411.90275Jin, Zhong; Gao, David Y. 2 2017 Analytic solutions to large deformation problems governed by generalized neo-Hookean model. Zbl 1382.49054Gao, David Yang 2 2017 Global solutions to spherically constrained quadratic minimization via canonical duality theory. Zbl 1382.49027Chen, Yi; Gao, David Yang 2 2017 Remarks on analytic solutions and ellipticity in anti-plane shear problems of nonlinear elasticity. Zbl 1382.49055Gao, David Yang 1 2017 Canonical duality method for solving Kantorovich mass transfer problem. Zbl 1382.49035Lu, Xiaojun; Gao, David Yang 1 2017 Canonical duality theory for solving non-monotone variational inequality problems. Zbl 1382.49034Liu, Guoshan; Gao, David Yang; Wang, Shouyang 1 2017 On d.c. optimization problems. Zbl 1382.49031Jin, Zhong; Gao, David Yang 1 2017 Canonical duality for solving general nonconvex constrained problems. Zbl 1362.90315Latorre, Vittorio; Gao, David Yang 12 2016 Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions. Zbl 1369.90133Chen, Yi; Gao, David Y. 4 2016 On the extrema of a nonconvex functional with double-well potential in 1D. Zbl 1369.35021Gao, David Yang; Lu, Xiaojun 3 2016 Global optimal trajectory in chaos and NP-hardness. Zbl 1345.34024Latorre, Vittorio; Gao, David Yang 3 2016 Analytical solutions to general anti-plane shear problems in finite elasticity. Zbl 1348.35265Yang Gao, David 3 2016 Global solutions to a class of CEC benchmark constrained optimization problems. Zbl 1345.90072Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua 1 2016 Mixed finite element solutions to contact problems of nonlinear Gao beam on elastic foundation. Zbl 1326.74075Gao, D. Y.; Machalová, J.; Netuka, H. 9 2015 Global solutions to fractional programming problem with ratio of nonconvex functions. Zbl 1338.90403Ruan, N.; Gao, D. Y. 4 2015 Canonical duality theory and triality for solving general global optimization problems in complex systems. Zbl 1321.49055Morales-Silva, Daniel; Gao, David 2 2015 Post-buckling solutions of hyper-elastic beam by canonical dual finite element method. Zbl 1298.74085Cai, Kun; Gao, David Y.; Qin, Qing H. 3 2014 Canonical duality approach for non-linear dynamical systems. Zbl 1323.92185Ruan, Ning; Gao, D. Y. 2 2014 Postbuckling analysis of a nonlinear beam with axial functionally graded material. Zbl 1359.74395Cai, Kun; Gao, David Y.; Qin, Qing H. 1 2014 Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems. Zbl 1364.90280Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua 1 2014 Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm. Zbl 1270.90041Gao, David Yang; Watson, Layne T.; Easterling, David R.; Thacker, William I.; Billups, Stephen C. 3 2013 Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in \(\mathbb{R}^n \). Zbl 1264.90143Morales-Silva, Daniel; Gao, David Yang 1 2013 On the triality theory for a quartic polynomial optimization problem. Zbl 1364.90271Gao, David Yang; Wu, Changzhi 10 2012 Canonical dual approach to solving the maximum cut problem. Zbl 1259.90154Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun 8 2012 Applying the canonical dual theory in optimal control problems. Zbl 1258.49058Zhu, Jinghao; Wu, Dan; Gao, David 4 2012 Optimization of matrix semirings for classification systems. Zbl 1244.16040Gao, D. Y.; Kelarev, A. V.; Yearwood, J. L. 8 2011 A novel canonical dual computational approach for prion AGAAAAGA amyloid fibril molecular modeling. Zbl 1397.92548Zhang, Jiapu; Gao, David Y.; Yearwood, John 5 2011 Solutions to quadratic minimization problems with box and integer constraints. Zbl 1222.90039Gao, David Yang; Ruan, Ning 13 2010 Canonical dual solutions for fixed cost quadratic programs. Zbl 1220.90072Gao, David Yang; Ruan, Ning; Sherali, Hanif D. 6 2010 Canonical dual least square method for solving general nonlinear systems of quadratic equations. Zbl 1200.90139Ruan, N.; Gao, David Y.; Jiao, Y. 4 2010 Global optimization by canonical dual function. Zbl 1223.90049Zhu, Jinghao; Zhou, Jiani; Gao, David 1 2010 Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality. Zbl 1213.90258Gao, David Yang; Ruan, Ning; Sherali, Hanif D. 24 2009 Global optimization for a class of fractional programming problems. Zbl 1206.90189Fang, Shu-Cherng; Gao, David Y.; Sheu, Ruey-Lin; Xing, Wenxun 20 2009 Traveling wave solutions to a reaction-diffusion equation. Zbl 1176.35100Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y. 11 2009 Canonical duality theory: connections between nonconvex mechanics and global optimization. Zbl 1220.90159Gao, David Y.; Sherali, Hanif D. 11 2009 A study on concave optimization via canonical dual function. Zbl 1279.90138Zhu, Jinghao; Tao, Shiming; Gao, David 4 2009 Solution to nonconvex quadratic programming with both inequality and box constraints. Zbl 1178.90268Zhang, Xi; Zhu, Jinghao; Gao, David Y. 2 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 2 2009 Canonical duality for solving nonconvex and nonsmooth optimization problem. Zbl 1171.65048Liu, Jing; Gao, David Y.; Gao, Yan 1 2009 Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem. Zbl 1143.74018Gao, D. Y.; Ogden, R. W. 17 2008 Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation. Zbl 1153.74032Gao, D. Y.; Ogden, R. W. 17 2008 Global extremal conditions for multi-integer quadratic programming. Zbl 1161.90457Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun 17 2008 Canonical dual approach to solving 0-1 quadratic programming problems. Zbl 1180.90195Fang, Shu-Cherng; Gao, David Yang; Sheu, Ruey-Lin; Wu, Soon-Yi 16 2008 Multi-scale modelling and canonical dual finite element method in phase transitions of solids. Zbl 1169.74518Gao, David Yang; Yu, Haofeng 15 2008 Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem. Zbl 1145.90054Gao, David Yang; Ruan, Ning 6 2008 The Korteweg-de Vries-Burgers equation and its approximate solution. Zbl 1157.65057Wang, Xiaohui; Feng, Zhaosheng; Debnath, Lokenath; Gao, David Y. 6 2008 Minimal distance between two non-convex surfaces. Zbl 1152.90552Gao, David Y.; Yang, Wei-Chi 4 2008 A nonconvex dissipative system and its applications. II. Zbl 1156.34005Feng, Zhaosheng; Gao, David Y. 1 2008 Solutions and optimality criteria to box constrained nonconvex minimization problems. Zbl 1171.90504Gao, David Yang 30 2007 Complete solutions and extremality criteria to polynomial optimization problems. Zbl 1104.90038Gao, David Yang 12 2006 Duality in distributed-parameter control of nonconvex and nonconservative dynamical systems with applications. Zbl 1112.49033Gao, David Yang 1 2006 Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints. Zbl 1140.90506Gao, David Yang 4 2005 Canonical duality theory and solutions to constrained nonconvex quadratic programming. Zbl 1075.90074Gao, David Yang 36 2004 Complementary principle, algorithm, and complete solutions to phase transitions in solids governed by Landau-Ginzburg equation. Zbl 1081.74037Gao, David Yang 3 2004 Tri-duality theory in phase transformations of ferroelectric crystals with random defects. Zbl 1183.74206Gao, David Y.; Li, Jie-Fang; Viehland, D. 1 2004 Perfect duality theory and complete solutions to a class of glocal optimization problems. Zbl 1040.49036Gao, David Yang 28 2003 Nonconvex semi-linear problems and canonical duality solutions. Zbl 1067.49024Gao, David Yang 12 2003 Complementarity, polarity and triality in non-smooth, non-convex and non-conservative Hamilton systems. Zbl 1097.49514Gao, David Yang 9 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 2 2001 Nonsmooth and nonconvex dynamics: Duality, polarity and complementary extremum principles. Zbl 0989.70016Gao, David Yang 1 2001 Duality principles in nonconvex systems. Theory, methods and applications. Zbl 0940.49001Gao, David Yang 44 2000 Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. Zbl 0983.74053Gao, David Yang 36 2000 Finite deformation beam models and triality theory in dynamical post-buckling analysis. Zbl 1068.74569Gao, David Yang 20 2000 Analytic solutions and triality theory for nonconvex and nonsmooth variational problems with applications. Zbl 0983.49024Gao, David Yang 19 2000 General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics. Zbl 0970.74011Gao, David Yang 12 1999 Pure complementary energy principle and triality theory in finite elasticity. Zbl 0992.74013Gao, David Yang 12 1999 Duality, triality and complementary extremum principles in non-convex parametric variational problems with applications. Zbl 0923.49017Gao, David Yang 14 1998 Bi-complementarity and duality: A framework in nonlinear equilibria with applications to the contact problem of elastoplastic beam theory. Zbl 0971.74059Gao, David Yang 5 1998 An extended beam theory for smart materials applications. II: Static formation problems. Zbl 0911.35039Gao, D. Y.; Russell, D. L. 4 1998 Nonlinear elastic beam theory with application in contact problems and variational approaches. Zbl 0843.73042Gao, David Yang 26 1996 Complementary finite-element method for finite deformation nonsmooth mechanics. Zbl 0857.73075Gao, David Yang 7 1996 An extended beam theory for smart material applications. I: Extended beam models, duality theory, and finite element simulations. Zbl 0856.73026Gao, D. Y.; Russell, D. L. 2 1996 Duality theory in nonlinear buckling analysis for von Kármán equations. Zbl 0832.73027Gao, David Yang 4 1995 Multi-duality in minimal surface-type problems. Zbl 0833.49023Gao, David Yang; Yang, Wei H. 3 1995 Stability and extremum principles for post yield analysis of finite plasticity. Zbl 0874.73027Gao, David Yang 1 1994 Global extremum criteria for finite elasticity. Zbl 0756.73035Gao, David Yang 5 1992 all cited Publications top 5 cited Publications all top 5 Cited by 282 Authors 43 Gao, David Yang 11 Zălinescu, Constantin 11 Zhu, Jinghao 9 Fang, Shu-Cherng 7 Sheu, Ruey-Lin 7 Xia, Yong 7 Xing, Wenxun 6 Ahn, Jeongho 5 Machalová, Jitka 5 Ruan, Ning 5 Shillor, Meir 4 Feng, Zhaosheng 4 Netuka, Horymír 4 Voisei, Mircea Dan 3 Cai, Kun 3 Jiao, Hongwei 3 Latorre, Vittorio 3 Li, Duan 3 Merodio, Jose 3 Neff, Patrizio 3 Spector, Scott J. 3 Zhou, Jiani 3 Zhou, Xiaojun 2 Ali, Elaf Jaafar 2 Aslan, İsmail 2 Baaser, Herbert 2 Bajer, Czesław I. 2 Birgin, Ernesto G. 2 Dai, Ning 2 Deng, Zhibin 2 Dyniewicz, Bartłomiej 2 Easterling, David R. 2 El Hamdaoui, Mustapha 2 Floudas, Christodoulos Achilleus 2 Gao, Yan 2 Kuttler, Kenneth L. jun. 2 Li, Chaojie 2 Lin, Gang-Xuan 2 Liu, Guohua 2 Liu, Jing 2 Liu, Sanyang 2 Lu, Xiaojun 2 Martin, Robert J. 2 Martínez, José Mario 2 M’Bengue, M’Bagne F. 2 Ogden, Raymond William 2 Park, Eun-Jae 2 Qin, Qinghua 2 Saad, Khaled Mohammed 2 Sahoo, Subhadarshan 2 Spector, Daniel E. 2 Sun, Bing 2 Sun, Xiaoling 2 Tac, Vahidullah 2 Tepole, Adrian B. 2 Voss, Jendrik 2 Wang, Zhenbo 2 Watson, Layne Terry 2 Wu, Changzhi 2 Wu, Dan 2 Xu, Ganjun 2 Xu, Yifan 2 Yang, Chunhua 2 Zhao, Shangrui 2 Zheng, Xiaojin 1 Al-Sharif, Eman Hussain Faissal 1 Andrews, Kevin T. 1 Andrica, Dorin 1 Arana-Jiménez, Manuel 1 Arqub, Omar Abu 1 Atangana, Abdon 1 Baek, Seungik 1 Bahrami, Fariba 1 Bai, Yanqin 1 Băleanu, Dumitru I. 1 Billups, Stephen C. 1 Blocken, Bert 1 Borrero, Juan S. 1 Borsos, Benjámin 1 Bouchitté, Guy 1 Brigadnov, Igor A. 1 Burkotová, Jana 1 Cai, Hongyan 1 Calve, Sarah 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 Chu, Ya-Chi 1 Colmegna, P. 1 Dagher, M. A. 1 Davini, Cesare 1 Desai, Jitamitra 1 DiPillo, Gianni 1 Du, Shouqiang 1 Dumont, Yves ...and 182 more Authors all top 5 Cited in 70 Serials 29 Journal of Global Optimization 9 Applied Mathematics and Computation 9 Journal of Industrial and Management Optimization 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Journal of Optimization Theory and Applications 8 Mathematics and Mechanics of Solids 8 Optimization Letters 7 Journal of Engineering Mathematics 5 Computer Methods in Applied Mechanics and Engineering 4 Acta Mechanica 4 Journal of Computational and Applied Mathematics 4 Optimization 4 Journal of Elasticity 4 Computational Optimization and Applications 4 Optimization and Engineering 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. 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(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 Filomat 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 European Journal of Mechanics. A. Solids 1 Communications in Nonlinear Science and Numerical Simulation 1 Computational Methods in Applied Mathematics 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 1 AIMS Mathematics 1 Fixed Point Theory and Algorithms for Sciences and Engineering all top 5 Cited in 25 Fields 101 Operations research, mathematical programming (90-XX) 69 Mechanics of deformable solids (74-XX) 38 Partial differential equations (35-XX) 38 Calculus of variations and optimal control; optimization (49-XX) 24 Numerical analysis (65-XX) 6 Systems theory; control (93-XX) 5 Ordinary differential equations (34-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) 3 Biology and other natural sciences (92-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Approximations and expansions (41-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-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 Information and communication theory, circuits (94-XX) Citations by Year