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Feasible descent algorithms for mixed complementarity problems. (English) Zbl 0946.90094
Summary: We consider a general algorithmic framework for solving nonlinear mixed complementarity problems. The main features of this framework are: (a) it is well-defined for an arbitrary mixed complementarity problem, (b) it generates only feasible iterates, (c) it has a strong global convergence theory, and (d) it is locally fast convergent under standard regularity assumptions. This framework is applied to the PATH solver in order to show viability of the approach. Numerical results for an appropriate modification of the PATH solver indicate that this framework leads to substantial computational improvements.

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49M37 Numerical methods based on nonlinear programming
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