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

Affiliation(s)

^{1}
Huarui College, Xinyang Normal University, Xinyang, China.

^{2}
School of Mathematics & Computational Science, Guilin University of Electronic Technology, Guilin, China.

^{3}
College of Science, Anhui University of Science and Technology, Huainan, China.

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.

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

Keywords

Mathematical Programs with Equilibrium Constraints, Conjugate Projection Gradient, Global Convergence, Superlinear Convergence

Mathematical Programs with Equilibrium Constraints, Conjugate Projection Gradient, Global Convergence, Superlinear Convergence

Cite this paper

Zhang, C. , Sun, L. , Zhu, Z. and Fang, M. (2015) An Implicit Smooth Conjugate Projection Gradient Algorithm for Optimization with Nonlinear Complementarity Constraints.*Applied Mathematics*, **6**, 1712-1726. doi: 10.4236/am.2015.610152.

Zhang, C. , Sun, L. , Zhu, Z. and Fang, M. (2015) An Implicit Smooth Conjugate Projection Gradient Algorithm for Optimization with Nonlinear Complementarity Constraints.

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