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非线性均衡问题一个超线性收敛的光滑逼近SQP算法

A Superlinear Convergent Smooth SQP Algotithm for Mathematical Programs with Nonlinear Equilibrium Constraints
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摘要 研究非线性均衡问题,引入一个磨光算子将原问题转化为光滑问题,并用此光滑问题来逼近原来的问题而求解.在每步迭代中,通过转轴运算,求解一个线性约束二次规划问题和显式修正方向来得到主方向,并通过一个显式公式来得到高阶修正方向使得算法避免Maratos效应.在不需要上层互补条件下证明了算法具有全局收敛性和强收敛性且具有超线性收敛速度. In this paper,mathematical programs with nonlinear equilibrium constraints are considered.By means of F-B function,the equilibrium constraints are transformed into a nonsmooth equation.Combining the idea of approximation with SQP method,a new approximate SQP method with explicit modify direction for mathematical programs with nonlinear equilibrium constraints is presented,and its global convergence and superlinear convergence are obtained without the upper-level strict complementarity condition.
作者 段复建 谭玲 朱志斌
机构地区 桂林电子科技大学数学与计算科学学院
出处 《应用数学》 CSCD 北大核心 2013年第2期277-291,共15页 Mathematica Applicata
基金 国家自然科学基金资助项目(11061011) 广西自然科学基金资助项目(2011GXNSFA018138)
关键词 均衡约束问题 互补约束问题 光滑SQP 全局收敛 超线性收敛 MPEC MPCC Smooth SQP method Global convergence Superlinear convergence
分类号 O224.2 [理学—运筹学与控制论]
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参考文献11

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二级参考文献24

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应用数学
2013年 第2期

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