Modified proximal-point method for nonlinear complementarity problems

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

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A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

International Journal of Operations Research and Information Systems ◽

10.4018/joris.2010070101 ◽

2010 ◽

Vol 1 (3) ◽

pp. 1-13

Author(s):

Ying Zhou ◽

Lizhi Wang

Keyword(s):

Numerical Experiments ◽

Proximal Point Algorithm ◽

Complementarity Problems ◽

Nonlinear Complementarity Problems ◽

New Method ◽

Proximal Method ◽

Proximal Point ◽

Nonlinear Complementarity ◽

Correction Step

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

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Particle Swarm Optimization-Proximal Point Algorithm for Nonlinear Complementarity Problems

Mathematical Problems in Engineering ◽

10.1155/2013/808965 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5

Author(s):

Chai Jun-Feng ◽

Wang Shu-Yan

Keyword(s):

Particle Swarm Optimization ◽

Proximal Point Algorithm ◽

Complementarity Problems ◽

Nonlinear Complementarity Problem ◽

Particle Swarm ◽

Nonlinear Complementarity Problems ◽

Particle Swarm Algorithm ◽

Proximal Point ◽

Swarm Optimization ◽

Nonlinear Complementarity

A new algorithm is presented for solving the nonlinear complementarity problem by combining the particle swarm and proximal point algorithm, which is called the particle swarm optimization-proximal point algorithm. The algorithm mainly transforms nonlinear complementarity problems into unconstrained optimization problems of smooth functions using the maximum entropy function and then optimizes the problem using the proximal point algorithm as the outer algorithm and particle swarm algorithm as the inner algorithm. The numerical results show that the algorithm has a fast convergence speed and good numerical stability, so it is an effective algorithm for solving nonlinear complementarity problems.

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