A Polyhedral Approach to the Single Row Facility Layout Problem

The Single Row Facility Layout Problem (SRFLP) is the problem of arranging facilities of given lengths on a line, while minimizing a weighted sum of the distances between all pairs of facilities. The SRFLP is strongly NP-hard and includes the well-known linear arrangement problem as a special case. We perform the first ever polyhedral study … Read more

A Newton-CG Augmented Lagrangian Method for Semidefinite Programming

We consider a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods. In order to analyze the rate of convergence of our proposed method, we characterize the Lipschitz continuity of the corresponding solution mapping at the origin. For the inner problems, we show that the positive … Read more

Tractable Robust Expected Utility and Risk Models for Portfolio Optimization

Expected utility models in portfolio optimization is based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance and support information. No additional assumption on the type of distribution such as normality is made. The investor’s utility is … Read more

On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods

The solution of KKT systems is ubiquitous in optimization methods and often dominates the computation time, especially when large-scale problems are considered. Thus, the effective implementation of such methods is highly dependent on the availability of effective linear algebra algorithms and software, that are able, in turn, to take into account specific needs of optimization. … Read more

Duality of ellipsoidal approximations via semi-infinite programming

In this work, we develop duality of the minimum volume circumscribed ellipsoid and the maximum volume inscribed ellipsoid problems. We present a unified treatment of both problems using convex semi–infinite programming. We establish the known duality relationship between the minimum volume circumscribed ellipsoid problem and the optimal experimental design problem in statistics. The duality results … Read more

Disjunctive Cuts for Non-Convex Mixed Integer Quadratically Constrained Programs

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 non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-and-project methodology. In particular, … Read more

Water Network Design by MINLP

We propose a solution method for a water-network optimization problem using a nonconvex continuous NLP (nonlinear programming) relaxation and a MINLP (mixed integer nonlinear programming) search. Our approach employs a relatively simple and accurate model that pays some attention to the requirements of the solvers that we employ. Our view is that in doing so, … Read more

Parallel implementation of a semidefinite programming solver based on CSDP on a distributed memory cluster

In this paper we present the algorithmic framework and practical aspects of implementing a parallel version of a primal-dual semidefinite programming solver on a distributed memory computer cluster. Our implementation is based on the CSDP solver and uses a message passing interface (MPI), and the ScaLAPACK library. A new feature is implemented to deal with … Read more

Homogeneous algorithms for monotone complementarity problems over symmetric cones

In \cite{aYOSHISE06}, the author proposed a homogeneous model for standard monotone nonlinear complementarity problems over symmetric cones and show that the following properties hold: (a) There is a path that is bounded and has a trivial starting point without any regularity assumption concerning the existence of feasible or strictly feasible solutions. (b) Any accumulation point … Read more

Information Relaxations and Duality in Stochastic Dynamic Programs

We describe a dual approach to stochastic dynamic programming: we relax the constraint that the chosen policy must be temporally feasible and impose a penalty that punishes violations of temporal feasibility. We describe the theory underlying this dual approach and demonstrate its use in dynamic programming models related to inventory control, option pricing, and oil … Read more