AN ALGORITHM FOR NONCONVEX PROGRAMMING
KRANNERT GRADUATE SCHOOL OF MANAGEMENT LAFAYETTE IN
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The paper presents an algorithm to solve the most general mathematical programming problem s.t. g superscript iy or 0, i 1,2,. ..,m, Min. gy, y y1,...,yn. The only restriction required is that the functions g superscript i, g be real valued. The general formulation allows for nonlinear or linear integer programming, mixed integer programming and general nonconvex continuous variable programming. The classical approaches have been essentially local or neighborhood techniques dependent on derivatives or finite difference approximations to derivatives. They suffer from two serious difficulties which can be characterized as the dimensionality problem and the problem of trapping at local optima. Our central aim here is to present a new framework for reaching global optimum. The procedure involves two interconnected mechanisms, a method for structuring the search and a decision rule for selecting the course of the search.
- Operations Research