TITLE:
An Implicit Smooth Conjugate Projection Gradient Algorithm for Optimization with Nonlinear Complementarity Constraints
AUTHORS:
Cong Zhang, Limin Sun, Zhibin Zhu, Minglei Fang
KEYWORDS:
Mathematical Programs with Equilibrium Constraints, Conjugate Projection Gradient, Global Convergence, Superlinear Convergence
JOURNAL NAME:
Applied Mathematics,
Vol.6 No.10,
September
18,
2015
ABSTRACT: 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.