Cutting Plane Selection with Analytic Centers and Multiregression

A cutting plane method from analytic centers for stochastic programming

The stochastic linear programming problem with recourse has a dual block angular structure. It can thus be handled by Benders decomposition or by Kelley's method of cutting planes; equivalently the dual problem has a primal block angular structure and can be handled by Dantzig-Wolfe decomposition| the two approaches are in fact identical by duality. Here we shall investigate the use of the meth...

Analytic Center Cutting-Plane Method

An Analytic Center Cutting Plane Method

Semideenite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as nding a point in a nonempty bounded convex body ? in the cone of symmetric positive semideenite matrices. Assume that ? is deened by an oracle, which, for any given m m symmetric matrix ^ Y , either connrms that ^ Y 2 ? or returns a cut, i.e., a symmetric matrix A...

Polynomial Cutting Plane Algorithms for Two-stage Stochastic Linear Programs Based on Ellipsoids, Volumetric Centers and Analytic Centers 1

Traditional simplex-basedalgorithms for two-stage stochastic linear programscan be broadly divided into two classes: (a) those that explicitly exploit the structure of the equivalent large-scale linear program and (b) those based on cutting planes (or equivalently on decomposition) that implicitly exploit that structure. Algorithms of class (b) are in general preferred. In 1988, following the w...

The Analytic Center Cutting Plane Method with Semidefinite Cuts

We analyze an analytic center cutting plane algorithm for the convex feasibility problems with semideenite cuts. At each iteration the oracle returns a p-dimensional semideenite cut at an approximate analytic center of the set of localization. The set of localization, which contains the solution set, is a compact set consists of piecewise algebraic surfaces. We prove that the analytic center is...