Data-Driven Reliable Facility Location Design

We study the reliable (uncapacitated) facility location (RFL) problem in a data-driven environment where historical observations of random demands and disruptions are available. Owing to the combinatorial optimization nature of the RFL problem and the mixed-binary randomness of parameters therein, the state-of-the-art RFL models applied to the data-driven setting either suggest overly conservative solutions, or … Read more

Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization

Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to nonconvex constraints. However, for a recently proposed subclass of such methods that is built on the popular stochastic-gradient methodology from the unconstrained setting, convergence guarantees have been … Read more

A new upper bound of the Euclidean TSP constant

Let X1, X2, . . . , Xn be n independent and uniformly distributed random points in a compact region R ⊂ R2 of area 1. Let TSP(X1, . . . , Xn) denote the length of the optimal Euclidean traveling salesman tour that traverses all these points. The classical Beardwood-Halton-Hammersley theorem proves the existence … Read more

Mixed-Integer Quadratic Optimization and Iterative Clustering Techniques for Semi-Supervised Support Vector Machines

Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more

On polynomial time solvability of combinatorial Markov random fields

The problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled as a mixed-integer program. This motivates us to study a general class of convex submodular optimization problems with indicator variables, which we show to be polynomially solvable in this paper. The key insight is that, possibly after … Read more