摘要
非光滑均衡问题包括很多优化问题,例如变分不等式问题、互补问题、约束为广义方程的数学规划问题、标准的约束优化问题等等。目前求解均衡问题的算法有邻近点算法、直接搜索法、投影收缩算法、光滑化投影梯度算法等,而交替束方法是一类求解目标函数具有可分离结构的有效算法,可以看成是一类特殊的邻近点法。针对均衡约束数学规划问题中的双层规划问题,首先最为核心的思想是应用参数极小化技术将该约束优化问题转化为一序列的极小化两个凸函数和的无约束单层优化问题;然后构造两个近似的子问题,应用交替束方法交替求解,最后建立算法的收敛性分析。
Nonsmooth equilibrium problems contain many kinds of optimization problems,such as finite-dimensional variational inequalities,complementarity problem,mathematical program with generalized equation constraint,standard constrained optimization problems,and so on.Recently there are proximal point methods,direct search methods,projection and contraction methods,and smoothing projected gradient methods to solve MPEC problems.An alternating bundle method is a kind of effective algorithm for solving minimization problems with separable substructures,and can be regarded as a kind of special adjacent point method to solve minimization problems with separable substructures.For bi-level programming in MPEC problems,the core idea is to transform the bi-level programming problems into sequential unconstrained one-level minimization problems which the objective function is the sum of two convex functions by parameter minimizing technique;then construct two approximate subproblems with the special structure and design a class of alternating bundle methods successively.Convergence analysis is also constructed at the end of the paper.
作者
李丹
LI Dan(College of Information Engineering,Dalian University,Dalian 116622,China)
出处
《大连大学学报》
2020年第6期79-83,共5页
Journal of Dalian University
基金
国家自然科学基金项目:非光滑非凸优化问题的交替线性化算法及其应用(11501074)。
关键词
非线性规划
非光滑优化
交替束方法
nonlinear programming
nonsmooth optimization
alternating bundle method
