Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstarting capabilities of active-set methods. We giv...

In this paper a simple derivation of duality is presented for convex quadratic programs with a convex quadratic constraint. This problem arises in a number of applications including trust region subproblems of nonlinear programming, regularized solution of ill-posed least squares problems, and ridge regression problems in statistical analysis. In general, the dual problem is a concave maximizat...

The problem of determining whether quadratic programming models possess either unique or multiple optimal solutions is important for empirical analyses which use a mathematical programming framework. Policy recommendations which disregard multiple optimal solutions (when they exist) are potentially incorrect and less than efficient. This paper proposes a strategy and the associated algorithm fo...

This paper studies the asymptotic behavior of the central path (X(ν), S(ν), y(ν)) as ν ↓ 0 for a class of degenerate semidefinite programming (SDP) problems, namely those that do not have strictly complementary primal-dual optimal solutions and whose “degenerate diagonal blocks” XT (ν) and ST (ν) of the central path are assumed to satisfy max{‖XT (ν)‖, ‖ST (ν)‖} = O(√ν). We establish the conver...

In this paper the problem of designing a xed state feedback control law which minimizes an upper bound on linear-quadratic performance measures for m distinct plants is reduced to a convex programming problem.

This paper presents scaled quadratic cuts based on scaling the second-order Taylor expansion terms for the decomposition methods Outer Approximation (OA) and Partial Surrogate Cuts (PSC) used for solving convex Mixed Integer Nonlinear Programing (MINLP). The scaled quadratic cut is proved to be a stricter and tighter underestimation for the convex nonlinear functions than the classical supporti...

A new optimality condition for minimization with general constraints is introduced. Unlike the KKT conditions, this condition is satissed by local minimizers of nonlinear programming problems, independently of constraint qualiications. The new condition implies, and is strictly stronger than, Fritz-John optimality conditions. Suu-ciency for convex programming is proved.

In this paper, we examine the duality gap between the robust counterpart of a primal uncertain convex optimization problem and the optimistic counterpart of its uncertain Lagrangian dual and identify the classes of uncertain problems which do not have a duality gap. The absence of a duality gap (or equivalently zero duality gap) means that the primal worst value equals the dual best value. We f...

We extend the target map, together with the weighted barriers and the notions of weighted analytic centers, from linear programming to general convex conic programming. This extension is obtained from a novel geometrical perspective of the weighted barriers, that views a weighted barrier as a weighted sum of barriers for a strictly decreasing sequence of faces. Using the Euclidean Jordan-algebr...