An Implicit Smooth Conjugate Projection Gradient Algorithm for Optimization with Nonlinear Complementarity Constraints

• 作者: Cong Zhang Limin Sun Minglei Fang Zhibin Zhu
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Mathematical Programs with Equilibrium CONSTRAINTS CONJUGATE PROJECTION Gradient Global CONVERGENCE SUPERLINEAR CONVERGENCE
• 年，卷（期）: 2015,（10）
• 页码范围: 1712-1726
• 页数: 15页
• 分类号: O1

摘要

This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.