Solving convex programs with infinitely many linear constraints by a relaxed cutting plane method

Relaxed Cutting Plane Method for Solving Linear Semi-Infinite Programming Problems

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...

Relaxed Cutting Plane Method for Solving Linear Semi-innnite Programming Problems

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

An Extended Cutting Plane Method for Solving Convex Minlp Problems

An extended version of Kelley’s cutting plane method is introduced in the present paper. The extended method can be applied for the solution of convex MINLP (mixed-integer non-linear programming) problems, while Kelley’s cutting plane method was originally introduced for the solution of convex NLP (non-linear programming) problems only. The method is suitable for solving large convex MINLP prob...

Solving variational inequalities defined on a domain with infinitely many linear constraints

We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed methods.

A cutting plane algorithm for solving bilinear programs