1. BIMATRIX EQUILIBRIUM POINTS AND MATHEMATICAL PROGRAMMING.
- Author
-
Lemke, C. E.
- Subjects
MATHEMATICAL programming ,NONLINEAR programming ,QUADRATIC programming ,MATRICES (Mathematics) ,MATHEMATICAL formulas ,MATHEMATICAL models ,SCHEMES (Algebraic geometry) ,ALGEBRAIC geometry ,MATHEMATICAL optimization ,GAME theory ,DIFFERENTIAL equations ,LINEAR programming - Abstract
Some simple constructive proofs are given of solutions to the matric system Mz - w = q; z ≧ 0; w ≧ 0; and z
T w = 0, for various kinds of data M, q, which embrace the quadratic programming problem and the problem of finding equilibrium points of bimatrix games. The general scheme is, assuming non-degeneracy, to generate an adjacent extreme point path leading to a solution. The scheme does not require that some functional be reduced. [ABSTRACT FROM AUTHOR]- Published
- 1965
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