A dual convex programming approach to solving linear programs with inequality constraints through entropic perturbation is derived. The amount of perturbation required depends on the desired accuracy of the optimum. The dual program contains only non-positivity constraints. An eoptimal solution to the linear program can be obtained effortlessly from the optimal solution of the dual program. Sin...

Linear optimization problems (LPs) with a very large or even infinite number of constraints frequently appear in many forms in machine learning. A linear program with m constraints can be written as min x∈P n c x with a where I assume for simplicity that the domain of x is the n dimensional probability simplex P n. Optimization problems with an infinite number of constraints of the form a j x ≤...

By considering the epigraphs of conjugate functions, we extend the Fenchel duality, applicable to a (possibly infinite) family of proper lower semicontinuous convex functions on a Banach space. Applications are given in providing fuzzy KKT conditions for semi-infinite programming.

One of the major computational tasks of using the traditional cutting plane approach to solve linear semi-infinite programming problems lies in finding a global optimizer of a nonlinear and nonconvex program. This paper generalizes the Gustafson and Kortanek scheme to relax this requirement. In each iteration, the proposed method chooses a point at which the infinite constraints are violated to...