Computational Experience and the Explanatory Value of Condition Numbers for Linear Optimization

The goal of this paper is to develop some computational experience and test the practical relevance of the theory of condition numbers C(d) for linear optimization, as applied to problem instances that one might encounter in practice. We used the NETLIB suite of linear optimization problems as a test bed for condition number computation and … Read more

A Robust Primal-Dual Interior-Point Algorithm for Nonlinear Programs

We present a primal-dual interior-point algorithm of line-search type for nonlinear programs, which uses a new decomposition scheme of sequential quadratic programming. The algorithm can circumvent the convergence difficulties of some existing interior-point methods. Global convergence properties are derived without assuming regularity conditions. The penalty parameter rho in the merit function is updated automatically such … Read more

A 1.52-Approximation Algorithm for the Uncapacitated Facility Location Problem

In this note we present an improved approximation algorithm for the (uncapacitated) metric facility location problem. This algorithm uses the idea of cost scaling, the greedy algorithm of \cite{JMS}, and the greedy augmentation procedure of \cite{CG,GK}. Citation Working Paper, MIT and the University of Iowa Article Download View A 1.52-Approximation Algorithm for the Uncapacitated Facility … Read more

Statistical inference of multistage stochastic programming problems

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. … Read more

Reformulating Linear Programs with Transportation Constraints — with Applications to Workforce Scheduling

We study linear programming models that contain transportation constraints in their formulation. Typically, these models have a multi-stage nature and the transportation constraints together with the associated flow variables are used to achieve consistency between consecutive stages. We describe how to reformulate these models by projecting out the flow variables. The reformulation can be more … Read more

Treewidth: Computational Experiments

Many NP-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for many optimization … Read more

Bounds on measures satisfying moment conditions

Given a semi algebraic set S of R^n we provide a numerical approximation procedure that yields upper and lower bounds on mu(S), for measures mu that satisfy some given moment conditions. The bounds are obtained as solutions of positive semidefinite programs that can be solved via standard software packages like the LMI MATLAB toolbox. Citation … Read more

Models and Solution Techniques for Frequency Assignment Problems

Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference … Read more

The Maximum Box Problem and its Application to Data Analysis

Given two finite sets of points $X^+$ and $X^-$ in $\R^n$, the maximum box problem consists in finding an interval (“box”) $B=\{x : l \leq x \leq u\}$ such that $B\cap X^-=\emptyset$, and the cardinality of $B\cap X^+$ is maximized. A simple generalization can be obtained by instead maximizing a weighted sum of the elements … Read more

A New Trust Region Technique for the Maximum Weight Clique Problem

A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a new trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of … Read more