A finitely converging cutting plane technique

Finitely Convergent Cutting Plane Methods for Solving the Quadratic Assignment Problem

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A Homogenized Cutting Plane Method

Cutting Plane Algorithms for Integer Programming, Cutting Plane Algorithms

Cutting plane methods are exact algorithms for integer programming problems. They have proven to be very useful computationally in the last few years, especially when combined with a branch and bound algorithm in a branch and cut framework. These methods work by solving a sequence of linear programming relax-ations of the integer programming problem. The relaxations are gradually improved to gi...

A Cutting-Plane Alternating Projections Algorithm A Cutting-Plane, Alternating Projections Algorithm for Conic Optimization Problems

We introduce a hybrid projection-localization method for solving large convex cone programs. The method interleaves a series of projections onto localization sets with the classical alternating projections method for convex feasibility problems; the problem is made amenable to the method by reducing it to a convex feasibility problem composed of a subspace and a cone via its homogeneous self-du...

A Primal Analogue of Cutting Plane Algorithms

This paper deals with algorithmic issues related to the design of an augmentation algorithm for general integer programs. It is shown that every phase of a primal method has a natural analogue in cutting plane algorithms. In particular, the role that the Chvv atal-Gomory cuts play in cutting plane algorithms is taken on by so-called Gomory-Young augmentation vectors. The latter family of vector...