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A projected-gradient interior-point algorithm for complementarity problems. (English) Zbl 1229.65097
The authors consider the following problem: Find $$x\in\mathbb{R}^n$$, $$y\in\mathbb{R}^n$$, $$w\in\mathbb{R}^n$$ such that $H(x,y,w)= 0,\;x_iw_i= 0,\;i= 1,2,\dots, n,\;x\geq 0,\;w\geq 0,\tag{1}$ where $$H: \mathbb{R}^{n+m+n}\to \mathbb{R}^{n+m}$$ is continuously differentiable. Many problems can be formutated in this form, e.g. linear and nonlinear complementarity problems, variational inequalities, KKT conditions of nonlinear programming. The authors propose the projected-gradient interior-point algorithm for solving problem (1). Convergence of the proposed algorithm is analyzed, special attention is devoted to linear problems. Computational experience with the algorithm for solving linear complementarity problems, as well as linear, quadratic and nonlinear programming problems are reported. Conclusions about the efficiency of the proposed methodology are included in the last section of the paper.

##### MSC:
 65K05 Numerical mathematical programming methods 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
##### Software:
MINOS; PDNET; LOQO; PATH Solver; CUTEr; GAMS
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