Abstract
We propose a new method to solve nonlinear semidefinite complementarity problem by combining a continuous method and a trust-region-type method. At every iteration, we need to calculate a second-order cone subproblem. We show the well-definedness of the method. The global convergent result is established.
Highlights
This paper deals with the semidefinite complementarity problem (SDCP) with respect to a mapping F : S → S, denoted by SDCP(F), to find an X ∈ S such that (X, F (X)) ∈ S+ × S+, ⟨X, F (X)⟩ = 0, (1)where S ⊂ Rn×n is a set comprising those X ∈ Rn×n that are real symmetric
We present a continuous and approximate method to solve SDCP(F)
We conclude that X∗ is a stationary point of the original problem. Another main step toward our global convergence result is contained in the following technical lemma
Summary
SDCP is the generalization of linear complementarity problems (LCPs) and semidefinite programs (SDPs) which has wide applications in engineering and economics [1]. There are two ways to derive the global convergence of an algorithm: trust-region methods and line search methods. Different from the above methods, we propose a new algorithm based on trust-region method to solve SDCPs. for any X, Y ∈ S. Abstract and Applied Analysis where (μ, X, Y) ∈ R × S × S and I is the n × n identity matrix This smoothing function was introduced by Kanzow [9] in the case of the NCP based on the Fischer-Burmeister function. We present a continuous and approximate method to solve SDCP(F).
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