Tight compact extended relaxations for nonconvex quadratic programming problems with box constraints

Cutting planes from the Boolean Quadric Polytope (BQP) can be used to reduce the optimality gap of the NP-hard nonconvex quadratic program with box constraints (BoxQP). It is known that all cuts of the Chvátal-Gomory closure of the BQP are A-odd cycle inequalities. We obtain a compact extended relaxation of all A-odd cycle inequalities, which … Read more

Approximation algorithms for the covering-type k-violation linear program

We study the covering-type k-violation linear program where at most $k$ of the constraints can be violated. This problem is formulated as a mixed integer program and known to be strongly NP-hard. In this paper, we present a simple (k+1)-approximation algorithm using a natural LP relaxation. We also show that the integrality gap of the … Read more

Mixed-Integer Linear Methods for Layout-Optimization of Screening Systems in Recovered Paper Production

The industrial treatment of waste paper in order to regain valuable fibers from which recovered paper can be produced, involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt … Read more

A Reliable Affine Relaxation Method for Global Optimization

An automatic method for constructing linear relaxations of constrained global optimization problems is proposed. Such a construction is based on affine and interval arithmetics and uses operator overloading. These linear programs have exactly the same numbers of variables and of inequality constraints as the given problems. Each equality constraint is replaced by two inequalities. This … Read more

A sufficient optimality criteria for linearly constrained, separable concave minimization problems

Sufficient optimality criteria for linearly constrained, concave minimization problems is given in this paper. Our optimality criteria is based on the sensitivity analysis of the relaxed linear programming problem. Our main result is similar to that of Phillips and Rosen (1993), however our proofs are simpler and constructive. Phillips and Rosen (1993) in their paper … Read more

A comparison of the Sherali-Adams, Lov\’asz-Schrijver and Lasserre relaxations for sh-1$ programming

Sherali and Adams \cite{SA90}, Lov\’asz and Schrijver \cite{LS91} and, recently, Lasserre \cite{Las01b} have proposed lift and project methods for constructing hierarchies of successive linear or semidefinite relaxations of a $0-1$ polytope $P\subseteq \oR^n$ converging to $P$ in $n$ steps. Lasserre’s approach uses results about representations of positive polynomials as sums of squares and the dual … Read more

Tighter Linear and Semidefinite Relaxations for Max-Cut Based on the Lov\’asz-Schrijver Lift-and-Project Procedure

We study how the lift-and-project method introduced by Lov\’az and Schrijver \cite{LS91} applies to the cut polytope. We show that the cut polytope of a graph can be found in $k$ iterations if there exist $k$ edges whose contraction produces a graph with no $K_5$-minor. Therefore, for a graph with $n\ge 4$ nodes, $n-4$ iterations … Read more