Global optimization algorithms for linearly constrained indefinite quadratic problems

Global Optimization Algorithms for Linearly Constrained Indefinite Quadratic Problems

1. I N T R O D U C T I O N Global optimization of constrained quadratic problems has been the subject of active research during the last two decades. Quadratic programming is a very old and important problem of optimization. It has numerous applications in many diverse fields of science and technology and plays a key role in many nonlinear programming methods. Nonconvex quadratic programming re...

Global optimization algorithms for bound constrained problems

An Algorithm for Global Minimization of Linearly Constrained Quadratic Functions

A branch and bound algorithm is proposed for finding an approximate global optimum of quadratic functions over a bounded polyhedral set. The algorithm uses Lagrangian duality to obtain lower bounds. Preliminary computational results are reported.

Simplified Copositive and Lagrangian Relaxations for Linearly Constrained Quadratic Optimization Problems in Continuous and Binary Variables

For a quadratic optimization problem (QOP) with linear equality constraints in continuous nonnegative variables and binary variables, we propose three relaxations in simplified forms with a parameter λ: Lagrangian, completely positive, and copositive relaxations. These relaxations are obtained by reducing the QOP to an equivalent QOP with a single quadratic equality constraint in nonnegative va...

Approximation Algorithms for Indefinite Complex Quadratic Maximization Problems

In this paper we consider the following two types of complex quadratic maximization problems: (i) maximize zHQz, subject to z k = 1, k = 1, ..., n, where Q is a Hermitian matrix with tr Q = 0 and z ∈ C is the decision vector; (ii) maximize Re yHAz, subject to y k = 1, k = 1, ..., p, and z l = 1, l = 1, ..., q, where A ∈ Cp×q and y ∈ C and z ∈ C are the decision vectors. In the real cases (namel...