|
Mixed Complementarity Problem
Mixed Complementarity Problem (MCP) is a problem formulation in mathematical programming. Many well-known problem types are special cases of, or may be reduced to MCP. It is a generalization of nonlinear complementarity problem (NCP). Definition The mixed complementarity problem is defined by a mapping F(x): \mathbb^n \to \mathbb^n, lower values \ell_i \in \mathbb \cup \ and upper values u_i \in \mathbb\cup\. The solution of the MCP is a vector x \in \mathbb^n such that for each index i \in \ one of the following alternatives holds: * x_i = \ell_i, \; F_i(x) \ge 0; * \ell_i < x_i < u_i, \; F_i(x) = 0; * . Another definition for MCP is: it is a variational inequality on the parallelepiped |
Mathematical Programming
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
