Solutions and optimality criteria to box constrained nonconvex minimization problems
Solutions and optimality criteria to box constrained nonconvex minimization problems
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DOI：
10.3934/jimo.2007.3.293
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发表时间：
2007-04
影响因子：
1.3
通讯作者：
D. Gao
中科院分区：
文献类型：
--
作者：
D. Gao
本文提出了一种用于解决受框约束的非凸多项式规划问题的规范对偶理论。证明在一定条件下，约束非凸问题可以转化为所谓的正则（完美）对偶问题，并可以用确定性方法求解。原问题的全局极值和局部极值都可以通过作者提出的三重性理论来识别。讨论了非凸整数规划和布尔最小二乘问题的应用。举例说明。提出了关于NP-hard问题的猜想。
This paper presents a canonical duality theory for solving nonconvex polynomial programming problems subjected to box constraints. It is proved that under certain conditions, the constrained nonconvex problems can be converted to the so-called canonical (perfect) dual problems, which can be solved by deterministic methods. Both global and local extrema of the primal problems can be identified by a triality theory proposed by the author. Applications to nonconvex integer programming and Boolean least squares problems are discussed. Examples are illustrated. A conjecture on NP-hard problems is proposed.