Euclidean Jordan-algebra is a commonly used tool in designing interiorpoint algorithms for symmetric cone programs. T -algebra, on the other hand, has rarely been used in symmetric cone programming. In this paper, we use both algebraic characterizations of symmetric cones to extend the target-following framework of linear programming to symmetric cone programming. Within this framework, we desi...

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

A disadvantage of the SDP (semidefinite programming) relaxation method for quadratic and/or combinatorial optimization problems lies in its expensive computational cost. This paper proposes a SOCP (second-order-cone programming) relaxation method, which strengthens the lift-and-project LP (linear programming) relaxation method by adding convex quadratic valid inequalities for the positive semid...

An algorithm for linear programming (LP) and convex quadratic programming (CQP) is proposed, based on an interior point iteration introduced more than ten years ago by J. Herskovits for the solution of nonlinear programming problems. Herskovits' iteration can be simpliied signiicantly in the LP/CQP case, and quadratic convergence from any initial point can be achieved. Interestingly the linear ...

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...

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...

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...

This paper presents a pivoting-based method for solving convex quadratic programming and then shows how to use it together with a parameter technique to solve mean-variance portfolio selection problems.