This paper describes necessary and suucient optimality conditions for bilevel programming problems with quadratic strictly convex lower levels. By examining the local geometry of these problems we establish that the set of feasible directions at a given point is composed of a nite union of convex cones. Based on this result, we show that the optimality conditions are simple generalizations of t...

This paper shows that the primal-dual steepest descent algorithm developed Zhu and Rockafellar for large-scale extended linear-quadratic programming can be used in solving constrained minimax problems related to a general C 2 saddle function. It is proved that the algorithm converges linearly from the very beginning of the iteration if the related saddle function is strongly convex-concave unif...

The convex hull relaxation (CHR) method (Albornoz 1998, Ahlatçıoğlu 2007, Ahlatçıoğlu and Guignard 2010) provides lower bounds and feasible solutions on convex 0-1 nonlinear programming problems with linear constraints. In the quadratic case, these bounds may often be improved by a preprocessing step that adds to the quadratic objective function terms that are equal to 0 for all 0-1 feasible so...

ABSTRACT. This paper describes a software package, called LOQO, which implements a primaldual interior-point method for general nonlinear programming. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programming with only brief mention of the extensions to convex and general nonlinear programming, since a detailed paper describing these extensions were publis...

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...

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...

DENG, ZHIBIN. Conic Reformulations and Approximations to Some Subclasses of Nonconvex Quadratic Programming Problems. (Under the direction of Dr. Shu-Cherng Fang.) In this dissertation, some subclasses of nonconvex quadratic programming problems are studied. We first study the nonconvex quadratic programming problem over the standard simplex with application to copositive matrix detection. A se...

A generalization of the weighted central path{following method for convex quadratic programming is presented. This is done by uniting and modifying the main ideas of the weighted central path{following method for linear programming and the interior point methods for convex quadratic programming. By means of the linear approximation of the weighted logarithmic barrier function and weighted inscr...

In this paper, the Iri-Imai algorithm for solving linear and convex quadratic programming is extended to solve some other smooth convex programming problems. The globally linear convergence rate of this extended algorithm is proved, under the condition that the objective and constraint functions satisfy a certain type of convexity (called the harmonic convexity in this paper). A characterizatio...

In this paper we present an algorithm of quasi-linear complexity for exactly calculating the infimal convolution of convex quadratic functions. The algorithm exactly and simultaneously solves a separable uniparametric family of quadratic programming problems resulting from varying the equality constraint.