We consider the use of quadratic approximate value functions for stochastic control problems with inputaffine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic programming policy in such cases requires the solution of an explicit convex optimization problem, such as a quadratic program, which can be carried out efficiently. We describe a simple and general metho...

A method for restoring an optical image which is subjected to low-pass frequency filtering is presented. It is assumed that the object whose image is restored is of finite spatial extent. The problem is treated as an algebraic image-restoration problem which is then solved as a quadratic programming problem with bounded variables. The regularization technique for the ill-posed system is to repl...

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...

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.