Robust canonical duality theory for solving nonconvex programming problems under data uncertainty

Shen Linsong; Wang Yanjun; Zhang Xiaomei

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Robust canonical duality theory for solving nonconvex programming problems under data uncertainty

机译：数据不确定性下非凸规划问题的鲁棒规范对偶理论

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This paper presents a robust canonical duality-triality theory for solving nonconvex programming problems under data uncertainty. This theory includes a robust canonical saddle-point theorem and robust canonical optimality conditions, which can be used to identify both robust global and local extrema of the primal problem. Two numerical examples are presented to illustrate that the robust Triality theory is particularly powerful for solving nonconvex optimization problems with data uncertainty.

机译：本文提出了一种鲁棒的规范对偶三元性理论，用于解决数据不确定性下的非凸规划问题。该理论包括鲁棒的规范鞍点定理和鲁棒的规范最优性条件，这些条件可用于识别原始问题的鲁棒全局和局部极值。给出了两个数值示例，说明了稳健的Triality理论对于解决具有数据不确定性的非凸优化问题特别有效。

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《Mathematical methods of operations research》 |2016年第1期|共22页
作者
Shen Linsong; Wang Yanjun; Zhang Xiaomei;
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正文语种 eng
中图分类运筹学;
关键词
Robust canonical duality-triality; Robust canonical optimality conditions; Nonconvex programming; Data uncertainty;

机译：鲁棒规范对偶三元性;鲁棒规范最优性条件;非凸规划;数据不确定性;

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2. Robust canonical duality theory for solving nonconvex programming problems under data uncertainty [J] . Shen Linsong, Wang Yanjun, Zhang Xiaomei Mathematical methods of operations research . 2016,第1期

机译：数据不确定性下非凸规划问题的鲁棒规范对偶理论
3. Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming [J] . DAVID YANG GAO Journal of Global Optimization . 2004,第4期

机译：典型对偶理论和约束非凸二次规划的解
4. Solving the canonical dual of box-and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm [J] . Gao D.Y., Watson L.T., Easterling D.R., Optimization methods & software . 2013,第1a3期

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5. Advances in Canonical Duality Theory and Applications in Global Optimization and NoncOnvex Systems(Abstract) [C] . Shu-Cherng Fang, David Y. Gao International Conference on Optimization: Techniques and Applications . 2007

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6. Stochastic programming approaches for decision-dependent uncertainty and gradual uncertainty resolution. [D] . Tarhan, Bora. 2009

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7. An accelerating algorithm for globally solving nonconvex quadratic programming [O] . Li Ge, Sanyang Liu -1

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8. Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming [O] . David Yang Gao 2004

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9. Canonical Duality Theory and Algorithms for Solving Some Challenging Problems in Global Optimization and Decision Science. [R] . Gao, D. Y. 2015

机译：全局优化决策科学中一些具有挑战性问题的典型对偶理论与算法。

Robust canonical duality theory for solving nonconvex programming problems under data uncertainty

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