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Global methods for nonlinear complementarity problems. (English) Zbl 0868.90127

Summary: Global methods for nonlinear complementarity problems formulate the problem as a system of nonsmooth nonlinear equations, or use continuation to trace a path defined by a smooth system of nonlinear equations. We formulate the nonlinear complementarity problem as a bound-constrained nonlinear least squares problem. Algorithms based on this formulation are applicable to general nonlinear complementarity problems, can be started from any nonnegative starting point, and each iteration only requires the solution of systems of linear equations. Convergence to a solution of the nonlinear complementarity problem is guaranteed under reasonable regularity assumptions. The convergence rate is \(Q\)-linear, \(Q\)-superlinear, or \(Q\)-quadratic, depending on the tolerances used to solve the subproblems.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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