In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, no single solution can adequately represent the whole set of optimal points. We propose a new efficient method for approximating the solution set of a convex quadratic multiobjective programming problem. The method is based on a warm-start interior point … Read more
We study approximation bounds for the SDP relaxation of quadratically constrained quadratic optimization: min f^0(x) subject to f^k(x)
In recent years, much work has been done on implementing a variety of algorithms in nonlinear programming software. In this paper, we analyze the performance of several state-of-the-art optimization codes on large-scale nonlinear optimization problems. Extensive numerical results are presented on different classes of problems, and features of each code that make it efficient or … Read more
We describe the object-oriented software package OOQP for solving convex quadratic programming problems (QP). The primal-dual interior point algorithms supplied by OOQP are implemented in a way that is largely independent of the problem structure. Users may exploit problem structure by supplying linear algebra, problem data, and variable classes that are customized to their particular … Read more
In this paper we present several new results on minimizing an indefinite quadratic function under quadratic/linear constraints. The emphasis is placed on the case where the constraints are two quadratic inequalities. This formulation is known as {\em the extended trust region subproblem}\/ and the computational complexity of this problem is still unknown. We consider several … Read more
We consider numerical methods for finding (weak) second-order critical points for large-scale non-convex quadratic programming problems. We describe two new methods. The first is of the active-set variety. Although convergent from any starting point, it is intended primarily for the case where a good estimate of the optimal active set can be predicted. The second … Read more
The following is a list of all of the published and unpublished works on quadratic programming that we are aware of. Some are general references to background material, while others are central to the development of the quadratic programming methods and to the applications we intend to cover in our evolving book on the subject. … Read more
Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation—one that has fewer constraints than the “standard” QP formulation—is available. We mention several instances of this class, including the known case in which the … Read more