A METHOD FOR APPROXIMATING THE SOLUTION SET OF A SYSTEM OF CONVEX INEQUALITIES BY POLYTOPES

[摘要] In this note a method for computing approximations by polytopes of the solution set Q of a system of convex inequalities is presented. It is shown that such approximations cnn be determined by an algorithm which converges in finitely many steps when the solution set of the given system of inequalities is bounded. In this case, the algorithm generates inner and outer approximations having the Hausdorff distance to each other (and to the set Q) no greater than an a priori fixed-epsilon and having their extreme points in partial derivative Q and in the relative exterior of Q, respectively.

[发布日期] 1991-09-24

[关键词] SIMPLEX;CONVEX SET;POLYTOPE;TRIANGULATION;REFINEMENT OF A TRIANGULATION;HAUSDORFF METRIC;G-MARGINAL VERTEX