scholarly journals Proximal point algorithm for nonlinear complementarity problem based on the generalized Fischer-Burmeister merit function

2013 ◽  
Vol 9 (1) ◽  
pp. 153-169 ◽  
Author(s):  
Yu-Lin Chang ◽  
◽  
Jein-Shan Chen ◽  
Jia Wu ◽  
Keyword(s):  
Complementarity Problem ◽  
Proximal Point Algorithm ◽  
Nonlinear Complementarity Problem ◽  
Merit Function ◽  
Proximal Point ◽  
Nonlinear Complementarity

scholarly journals Particle Swarm Optimization-Proximal Point Algorithm for Nonlinear Complementarity Problems

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.

On an application of the complex nonlinear complementarity problem

1976 ◽  
Vol 15 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Minimization Problem ◽  
Complementarity Problem ◽  
Complex Space ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Polyhedral Cones ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

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