The Mixed Complementarity Problem, or MCP is a fundamental problem in optimization that encompasses many of the continuous optimization problems special cases. It is useful for expressing systems of nonlinear inequalities and equations; the complementarity also allows boundary conditions be to specified in a succinct manner. Problems of this type occur in many branches of the sciences, including mathematics, engineering, economics, operations research, and computer science. Some futher details on algorithms and related literature can be found at CPNET.
Some of the algorithmic ideas for systems of nonlinear equations are also relevant here:
Trust Region and Line-search
Methods
Related Topics:
Nondifferentiable Optimization
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Updated 15 September 1997