Robust Critical Node Selection by Benders Decomposition

The critical node selection problem (CNP) has important applications in telecommunication, supply chain design, and disease propagation prevention. In practice, the weights on the connections are either uncertain or hard to estimate so recently robust optimization approaches have been considered for CNP. In this article, we address very general uncertainty sets, only requiring a linear … Read more

A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems, with Convergence Proofs

We present an infeasible primal-dual interior point method for semidefinite optimization problems, making use of constraint reduction. We show that the algorithm is globally convergent and has polynomial complexity, the first such complexity result for primal-dual constraint reduction algorithms for any class of problems. Our algorithm is a modification of one with no constraint reduction … Read more

Inventory control for a perishable product with non-stationary demand and service level constraints

We study the practical production planning problem of a food producer facing a non-stationary erratic demand for a perishable product with a fixed life time. In meeting the uncertain demand, the food producer uses a FIFO issuing policy. The food producer aims at meeting a certain service level at lowest cost. Every production run a … Read more

The viewshed problem: a theoretical analysis and a new algorithm for finding the viewshed of a given point on a triangulated terrain

We give a comprehensive theoretical treatment for calculating the viewshed of a given point, present an analytical solution to the viewshed problem and a new algorithm for finding the viewshed on a triangulated terrain. We implement our algorithm on a real terrain. Some algorithms make use of the horizon information of the terrain to calculate … Read more

A Flexible Inexact Restoration Method and Application to Optimization with Multiobjective Constraints under Weighted-Sum Scalarization

We introduce a new flexible Inexact-Restoration (IR) algorithm and an application to problems with multiobjective constraints (MOCP) under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. This is done in … Read more

Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization

This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but convex) component. In order to solve these problems, we propose a randomized stochastic projected gradient (RSPG) algorithm, in which proper mini-batch of samples are … Read more

A Semidefinite Hierarchy for Containment of Spectrahedra

A spectrahedron is the positivity region of a linear matrix pencil, thus defining the feasible set of a semidefinite program. We propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in another one. This approach comes from applying a moment relaxation to a suitable polynomial optimization formulation. The … Read more

A Sequential Quadratic Optimization Algorithm with Rapid Infeasibility Detection

We present a sequential quadratic optimization (SQO) algorithm for nonlinear constrained optimization. The method attains all of the strong global and fast local convergence guarantees of classical SQO methods, but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances. A two-phase strategy, carefully constructed … Read more

Practical Portfolio Optimization

This paper is on the portfolio optimization problem for which two generic models are presented in the context of a proprietary solver called GENO: the first is a pseudo-dynamic model meant for the single holding-period case; the second is a truly dynamic model that applies to both the single and the multi-period scenario. Both models … Read more

A Short Proof of Strassen’s Theorem Using Convex Analysis

We give a simple proof of Strassen’s theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and provides an additional, intuitive optimization formulation for stochastic dominance. Citation Northwestern Univ., Aug., 2013 Article Download View A Short Proof of Strassen's Theorem Using Convex … Read more