This paper presents an improved as well as a completely new version of a mixed integer linear programming (MILP) formulation for solving the quadratic assignment problem (QAP) to global optimum. Both formulations work especially well on instances where at least one of the matrices is sparse. Modification schemes, to decrease the number of unique elements per row in symmetric instances, are pres...

We study a polytope which arises from a mixed integer programming formulation of the quadratic semi-assignment problem. We introduce an isomorphic projection in order to transform the polytope to another essentially equivalent and tractable polytope. As a result, some basic polyhedral properties, such as the dimension, the affine hull, and the trivial facets, are obtained in quite a simple way....

This paper deals with the solution of the discretized quasistatic 3D Signorini problems with local Coulomb friction. After a time discretization we obtain a system of static contact problems with Coulomb friction. Each of these problems is decomposed by the TFETI domain decomposition method used in auxiliary contact problemswith Tresca friction. The algebraic formulation of these problems in 3D...

We study the convex hull of a set arising as a relaxation of difficult convex mixed integer quadratic programs (MIQP). We characterize the extreme points of our set and the extreme points of its continuous relaxation. We derive four quadratic cutting surfaces that improve the strength of the continuous relaxation. Each of the cutting surfaces is second-order-cone representable. Via a shooting e...

This paper presents a novel approach to tackle the problem of optimal neutral wire grounding in bipolar DC networks including asymmetric loading, which naturally involves mixed-integer nonlinear programming (MINLP) and is challenging solve. MINLP model transformed into recursive quadratic (MIQ) by linearizing hyperbolic relation between voltage powers constant power terminals. A algorithm imple...

We study several joint facility location and inventory management problems with stochastic retailer demand. In particular, we consider cases with uncapacitated facilities, capacitated facilities, correlated retailer demand, stochastic lead times, and multicommodities. We show how to formulate these problems as conic quadratic mixed-integer problems. Valid inequalities, including extended polyma...

The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem that has a natural formulation as a Mixed Integer Quadratically Constrained Program. This MIQCP is closely related to the Quadratic Assignment Problem and, as far as we know, has not received any attention yet. We show in this article that such a formulation has interesting theoretical properties. Its QP rel...

Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of risk. From the perspective of qualitative robustness theory, we discuss sufficient conditions for continuity of the resulting objective functions with respect ...

We describe here a method for building a support vector machine (SVM) with integer parameters. Our method is based on a branchand-bound procedure, derived from modern mixed integer quadratic programming solvers, and is useful for implementing the feedforward phase of the SVM in fixed–point arithmetic. This allows the implementation of the SVM algorithm on resource–limited hardware like, for exa...

Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly as feasible regions MICP problems. We establish several results this direction, including first complete characterization mixed-binary case a simple necessary condition general case. use latter to derive non-representa...