Alternative Theorems for Quadratic Inequality Systems and Global Quadratic Optimization

Alternative Theorems for Quadratic Inequality Systems and Global Quadratic Optimization

We establish alternative theorems for quadratic inequality systems. Consequently, we obtain Lagrange multiplier characterizations of global optimality for classes of non-convex quadratic optimization problems. We present a generalization of Dine’s theorem to a system of two homogeneous quadratic functions with a regular cone. The class of regular cones are cones K for which (K∪−K) is a subspace...

Approximating Global Quadratic Optimization with Convex Quadratic Constraints

We consider the problem of approximating the global maximum of a quadratic program (QP) subject to convex non-homogeneous quadratic constraints. We prove an approximation quality bound that is related to a condition number of the convex feasible set; and it is the currently best for approximating certain problems, such as quadratic optimization over the assignment polytope, according to the bes...

Global Quadratic Optimization via Conic Relaxation

We present a convex conic relaxation for a problem of maximizing an indefinite quadratic form over a set of convex constraints on the squared variables. We show that for all these problems we get at least 12 37 -relative accuracy of the approximation. In the second part of the paper we derive the conic relaxation by another approach based on the second order optimality conditions. We show that ...

Nonconvex All-Quadratic Global Optimization Problems:

A Semidefinite Optimization Approach to Quadratic Fractional Optimization with a Strictly Convex Quadratic Constraint

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...