Range-space methods for convex quadratic programming improve in efficiency as the number of constraints active at the solution decreases. In this paper we describe a range-space method based upon updating a weighted Gram-Schmidt factorization of the constraints in the active set. The updating methods described are applicable to both primal and dual quadratic programming algorithms that use an a...

Let (QP ) be an integer quadratic program that consists in minimizing a quadratic function subject to linear constraints. In this paper, we present several linearizations of (QP ). Many linearization methods for the quadratic 0-1 programs are known. A natural approach when considering (QP ) is to reformulate it into a quadratic 0-1 program. However, this method, that we denote BBL (Binary Binar...

Linear model predictive control (MPC) assumes a linear system model, that the constraints sets are representable via linear inequalities and that the objective function is convex quadratic. Linear MPC is appealing because the associated optimisation problem typically solved at each time interval may be expressed as a convex quadratic program, which can be solved efficiently online. Topics not c...

In this paper we discuss problems with quadratic objective function, one or two quadratic constraints, and, possibly, some additional linear constraints. In particular, we consider cases where the Hessian of the quadratic functions are simultaneously diagonalizable, so that the objective and constraint functions can all be converted into separable functions. We give conditions under which a sim...

General quadratic matrix minimization problems, with orthogonal constraints, arise in continuous relaxations for the (discrete) quadratic assignment problem (QAP). Currently, bounds for QAP are obtained by treating the quadratic and linear parts of the objective function, of the relaxations, separately. This paper handles general objectives as one function. The objectives can be both nonhomogen...

In this paper, we establish global optimality conditions for quadratic optimization problems with quadratic equality and bivalent constraints. We first present a necessary and sufficient condition for a global minimizer of quadratic optimization problems with quadratic equality and bivalent constraints. Then, we examine situations where this optimality condition is equivalent to checking the po...