Quadratic programming (QP) is an optimization problem wherein one minimizes (or maximizes) a quadratic function of a finite number of decision variable subject to a finite number of linear inequality and/ or equality constraints. In this paper, a quadratic programming problem (FFQP) is considered in which all cost coefficients, constraints coefficients, and right hand side are characterized by ...

The application of multi-attribute utility theory based on the Choquet integral requires the prior identification of a capacity if the utility scale is unipolar, or of a bi-capacity if the utility scale is bipolar. In order to implement a minimum distance principle for capacity or bi-capacity approximation or identification, quadratic distances between capacities and bi-capacities are studied. ...

In the framework of multi-criteria decision making whose aggregation process is based on the Choquet integral, we present a maximum entropy like method enabling to determine, if it exists, the “least specific” capacity compatible with the initial preferences of the decision maker. The proposed approach consists in solving a strictly convex quadratic program whose objective function is equivalen...

We propose a method called Polynomial Quadratic Convex Reformulation (PQCR) to solve exactly unconstrained binary polynomial problems (UBP) through quadratic convex reformulation. First, we quadratize the problem by adding new variables and reformulating into non-convex program with linear constraints (MIQP). then consider solution of (MIQP) specially-tailored reformulation method. In particula...

In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they lift the original n×n-dimensional variable to an n2×n2-dimensional variable, which limits their practical applicability. In contrast, here we present a lifti...

Recent papers have shown the equivalence of several tractable bounds for Boolean quadratic programming. In this note we give simpliied proofs for these results, and also show that all of the bounds considered are simultaneously attained by one diagonal perturbation of the quadratic form.

Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker's, Cottle's and Dantzig's principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program. A nite criss-cross method, based on least{index resolution, is constructed for solving the LCP. In proving nitenes...