Abstract
A generalized Newton method for the solution of a kind of complementarity problem is given. The method is based on a nonsmooth equations reformulation of the problem byF-Bfunction and on a generalized Newton method. The merit function used is a differentiable function. The global convergence and superlinear local convergence results are also given under suitable assumptions. Finally, some numerical results and discussions are presented.
Highlights
This paper considers a kind of complementarity problem:F (x) ≥ 0, G (x) ≥ 0, ⟨F (x), G (x)⟩ = 0, (1)where F : Rn → Rn, G : Rn → Rn are two differentiable functions
When G(x) = x, (1) reduces to the nonlinear complementarity problem, which is a general framework for optimality conditions of nonlinear optimization problems as well as some problems arising in different fields
Some research work has been devoted to techniques for globalizing the local methods
Summary
This paper considers a kind of complementarity problem:. where F : Rn → Rn, G : Rn → Rn are two differentiable functions. This paper considers a kind of complementarity problem:. In the past few years, several theoretical and computational results for complementarity have been established, such as [1,2,3,4,5,6,7,8,9,10,11,12]. The method is based on semismooth equations reformulation of (1). Some research work has been devoted to techniques for globalizing the local methods. In this paper, we are interested in solving (1) by a Newton based method. The method is based on a line search and a semismooth equations reformulation of (1). (1) is converted into a semismooth equation. A generalized Newton method for solving the reformulation is introduced.
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