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The viscosity approximation to the Hamilton-Jacobi-Bellman equation in optimal feedback control: Upper bounds for extended domains
Global optimization algorithm for solving bilevel programming problems with quadratic lower levels
1. | Department of Mathematics, University of Trier, 54286 Trier, Germany, Germany |
[1] |
Jing Zhou, Zhibin Deng. A low-dimensional SDP relaxation based spatial branch and bound method for nonconvex quadratic programs. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2087-2102. doi: 10.3934/jimo.2019044 |
[2] |
Yue Zheng, Zhongping Wan, Shihui Jia, Guangmin Wang. A new method for strong-weak linear bilevel programming problem. Journal of Industrial and Management Optimization, 2015, 11 (2) : 529-547. doi: 10.3934/jimo.2015.11.529 |
[3] |
Bhawna Kohli. Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3209-3221. doi: 10.3934/jimo.2020114 |
[4] |
Le Thi Hoai An, Tran Duc Quynh, Pham Dinh Tao. A DC programming approach for a class of bilevel programming problems and its application in Portfolio Selection. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 167-185. doi: 10.3934/naco.2012.2.167 |
[5] |
Ye Tian, Cheng Lu. Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems. Journal of Industrial and Management Optimization, 2011, 7 (4) : 1027-1039. doi: 10.3934/jimo.2011.7.1027 |
[6] |
Dan Xue, Wenyu Sun, Hongjin He. A structured trust region method for nonconvex programming with separable structure. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 283-293. doi: 10.3934/naco.2013.3.283 |
[7] |
Xiaoni Chi, Zhongping Wan, Zijun Hao. Second order sufficient conditions for a class of bilevel programs with lower level second-order cone programming problem. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1111-1125. doi: 10.3934/jimo.2015.11.1111 |
[8] |
Yibing Lv, Tiesong Hu, Jianlin Jiang. Penalty method-based equilibrium point approach for solving the linear bilevel multiobjective programming problem. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1743-1755. doi: 10.3934/dcdss.2020102 |
[9] |
Nazih Abderrazzak Gadhi. A note on the paper "Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem". Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021103 |
[10] |
Ziye Shi, Qingwei Jin. Second order optimality conditions and reformulations for nonconvex quadratically constrained quadratic programming problems. Journal of Industrial and Management Optimization, 2014, 10 (3) : 871-882. doi: 10.3934/jimo.2014.10.871 |
[11] |
Yang Li, Yonghong Ren, Yun Wang, Jian Gu. Convergence analysis of a nonlinear Lagrangian method for nonconvex semidefinite programming with subproblem inexactly solved. Journal of Industrial and Management Optimization, 2015, 11 (1) : 65-81. doi: 10.3934/jimo.2015.11.65 |
[12] |
Yang Li, Liwei Zhang. A nonlinear Lagrangian method based on Log-Sigmoid function for nonconvex semidefinite programming. Journal of Industrial and Management Optimization, 2009, 5 (3) : 651-669. doi: 10.3934/jimo.2009.5.651 |
[13] |
Z.G. Feng, K.L. Teo, Y. Zhao. Branch and bound method for sensor scheduling in discrete time. Journal of Industrial and Management Optimization, 2005, 1 (4) : 499-512. doi: 10.3934/jimo.2005.1.499 |
[14] |
Nguyen Van Thoai. Decomposition branch and bound algorithm for optimization problems over efficient sets. Journal of Industrial and Management Optimization, 2008, 4 (4) : 647-660. doi: 10.3934/jimo.2008.4.647 |
[15] |
Zhiguo Feng, Ka-Fai Cedric Yiu. Manifold relaxations for integer programming. Journal of Industrial and Management Optimization, 2014, 10 (2) : 557-566. doi: 10.3934/jimo.2014.10.557 |
[16] |
Qinghong Zhang, Gang Chen, Ting Zhang. Duality formulations in semidefinite programming. Journal of Industrial and Management Optimization, 2010, 6 (4) : 881-893. doi: 10.3934/jimo.2010.6.881 |
[17] |
Charles Fefferman. Interpolation by linear programming I. Discrete and Continuous Dynamical Systems, 2011, 30 (2) : 477-492. doi: 10.3934/dcds.2011.30.477 |
[18] |
Yi Xu, Wenyu Sun. A filter successive linear programming method for nonlinear semidefinite programming problems. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 193-206. doi: 10.3934/naco.2012.2.193 |
[19] |
Jing Zhou, Cheng Lu, Ye Tian, Xiaoying Tang. A SOCP relaxation based branch-and-bound method for generalized trust-region subproblem. Journal of Industrial and Management Optimization, 2021, 17 (1) : 151-168. doi: 10.3934/jimo.2019104 |
[20] |
Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473 |
2021 Impact Factor: 1.411
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