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

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DOI: 10.4236/am.2015.610152    2,608 Downloads   2,932 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

References

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