‎In this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎The proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the Newton equation system‎, ‎by using an inexact Newton direction‎. ‎Furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

In this paper, the authors solve the two stage stochastic programming with separable objective by obtaining convex polynomial approximations to the convex objective function with an arbitrary accuracy. Our proposed method will be valid for realistic applications, for example, the convex objective can be either non-differentiable or only accessible by Monte Carlo simulations. The resulting polyn...

the problem of utilizing undesirable (bad) outputs in dea models often need replacing the assumption of free disposability of outputs by weak disposability of outputs. the kuosmanen technology is the only correct representation of the fully convex technology exhibiting weak disposability of bad and good outputs. also, there are some specific features of non-radial data envelopment analysis (dea...

In this paper, we aim to prove the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a mild calmness condition, which holds automatically for convex composite piecewise linear-quadratic programming, we establish the global Q-linear rate of convergence for a general semi-proximal ADMM w...

The quadratic bilevel programming problem is an instance of a quadratic hierarchical decision process where the lower level constraint set is dependent on decisions taken at the upper level. By replacing the inner problem by its corresponding KKT optimality conditions, the problem is transformed to a single yet non-convex quadratic program, due to the complementarity condition. In this paper we...

We propose an algorithm to locate an object with unknown coordinates based on the positive semi-definite programming in the wireless sensor networks, assuming that the squared error of the measured distance follows Gaussian distribution. We first obtain the estimator of the object location; then transform the non-convex problem to convex one by the positive semi-definite relaxation; and finally...

This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and nonconvex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the liftand...

Abstract: We consider the non-parametric maximum likelihood estimation in the class of Polya frequency functions of order two, viz. the densities with a concave logarithm. This is a subclass of unimodal densities and fairly rich in general. The NPMLE is shown to be the solution to a convex programming problem in the Euclidean space and an algorithm is devised similar to the iterative convex min...

Characterizations of global optimality are given for general difference convex (DC) optimization problems involving convex inequality constraints. These results are obtained in terms of E-subdifferentials of the objective and constraint functions and do not require any regularity condition. An extension of Farkas’ lemma is obtained for inequality systems involving convex functions and is used t...

Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many properties of convex hulls in Euclidean space fail to transfer over. We give examples of some such properties. For 2-dimensional CAT(0) polyhedral complexes, we gi...