MIXED CONVEX AND NON-CONVEX PROGRAMMING.
Themis optimization research program (Final),
TEXAS A AND M UNIV COLLEGE STATION INST OF STATISTICS
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In the paper an algorithm is described for solving mixed convex-nonconvex programming problems of the form minimize f sub ox, y subject to f sub jx, y or 0, j 1, ..., k, where x is an n-vector and y is an m-vector and, in addition to some other mild conditions, for each y, f sub jx, y, j 0, ..., k, is a convex function of x. The algorithm consists of an efficient scan of the non-convex y space in conjunction with convex programming methods in the convex x space to find the global minimum of f sub o with a reasonable amount of computational effort. The algorithm will be practicable only when the number m of non-convex variables is moderate, say m or 5.
- Operations Research