Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming

Abstract

This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy. Instead of specifying the feasible region by a set of convex inequalities,fi(x)_ bi, i=1, 2, , m, the feasible region is defined via set containment. Here n convex activity sets {Kj, j=1, 2, * * *, n} and a convex resource set K are specified and the feasible region is given by