An interior point method for the nonlinear complementarity problem
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- 作者：Iusem ; Alfredo Noel
- 关键词：Variational inequalities ; Nonlinear complementarity ; Interior point methods ; Monotone operators ; Convex programming ; Generalized distances
- 刊名：Applied Numerical Mathematics
- 出版年：1997
- 出版时间：September, 1997
- 年：1997
- 卷：24
- 期：4
- 页码：469-482
- 全文大小：667 K
文摘
We present an interior point method for the nonlinear complementarity problem which converges, whenever the problem has solutions, for any paramonotone operator (i.e., monotone and such that that 
F(x)−F(y), x − y
= 0 implies F(x) = F(y)). The iterative step consists of easily computable closed formulae, up to a finite search for a real parameter. Convergence of the algorithm results from its reduction to an interior point method for variational inequalities using Bregman functions, whose iterative step requires a similar finite search plus the solution of a nonlinear equation in one real variable. As an intermediate step in the reduction, we simplify the method for variational inequalities, replacing the solution of the nonlinear equation by a second finite search for another real parameter, which is finally replaced by a closed formula in the case of nonlinear complementarity problems.
F(x)−F(y), x − y = 0 implies F(x) = F(y)). The iterative step consists of easily computable closed formulae, up to a finite search for a real parameter. Convergence of the algorithm results from its reduction to an interior point method for variational inequalities using Bregman functions, whose iterative step requires a similar finite search plus the solution of a nonlinear equation in one real variable. As an intermediate step in the reduction, we simplify the method for variational inequalities, replacing the solution of the nonlinear equation by a second finite search for another real parameter, which is finally replaced by a closed formula in the case of nonlinear complementarity problems.