Zhang, C., Sun, L.M., Zhu, Z.B. and Fang, M.L. (2015) Levenberg-Marquardt Method for Mathematical Programs with Linearly Complementarity Constraints. American Journal of Computational Mathematics, 5, 239-242.
http://dx.doi.org/10.4236/ajcm.2015.53020

has been cited by the following article:

• 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.