September 2026 – Page 4 – Optimization Online

Dantzig-Wolfe Decomposition for Monotone Two-Stage Stochastic Mixed-Integer Programs Applied to a Power Distribution System Resilience Problem

Published: 2026/09/04, Updated: 2026/09/07

Stochastic Programming dantzig-wolfe decomposition, distribution system resilience, extreme-weather events, mobile power sources, monotonicity, stochastic programming

We develop a novel Dantzig-Wolfe (DW) decomposition algorithm for monotone two-stage stochastic mixed-integer programs (SMIPs). The key novelty in this algorithm is to relax the non-anticipativity constraints (NACs) in line with the monotonicity in the problem. We prove (i) that the relaxed restricted master problem (RMP) faster identifies dominated columns that cannot improve the RMP … Read more

An optimal orbit design for LISA

Published: 2026/09/03

Yaguang Yang

Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs constrained nonlinear optimization, formation fly, optimal orbit design

The ESA/NASA joint LISA (laser interferometer space antenna) mission is designed to detect gravitational waves to perform gravitational astronomy. A key mission requirement is the maintenance of a three-spacecraft constellation in a near-equilateral triangular configuration with a prescribed inter-spacecraft separation. Existing approaches have addressed this problem using simplified dynamical models to enhance tractability; however, the … Read more

Calculus of the facial distance

Published: 2026/09/02

Javier F. Peña

Convex and Nonsmooth Optimization, Polyhedra Calculus, facial distance, frank-wolfe

We develop a few calculus rules to compute or lower bound the facial distance of a polytope. We illustrate our calculus rules on various popular polytopes. In particular, we provide a lower bound on the facial distance of the Birkhoff polytope. CitationWorking paper. Tepper School of Business. Carnegie Mellon UniversityArticleDownload View PDF

Convergence rate of the moment-SOS hierarchy for univariate polynomial optimization

Published: 2026/09/02

Global Optimization Theory, Semi-definite Programming polynomial optimization; moments; sums-of-squares

We study the convergence rate of the moment-SOS (sum-of-squares) hierarchy for polynomial optimization problems (POPs) on a bounded subset of the real line described by arbitrary polynomial inequalities. We prove that, for every fixed univariate POP, the relaxation error is bounded by $O(1/r^2)$, where $r$ is the relaxation order. In particular, boundary degeneracies in the … Read more

On the Equivalence of Monge and Kantarovich Problems in Discrete Optimal Transport

Published: 2026/09/01

Thirumulanathan Dhayaparan

Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization of Systems modeled by PDEs

Consider a discrete optimal transport problem that has at least two consumers. We show that the Monge and Kantorovich versions of such a discrete optimal transport problem are equivalent for all cost functions if and only if the supply from all the suppliers are equal, and the demand from every consumer is an integral multiple … Read more

Fixed charges of arbitrary sign: what survives and what fails

Published: 2026/09/01

Duy T. Nguyen

(Mixed) Integer Linear Programming, Polyhedra, Production and Logistics fixed-charge problems, integral polyhedra, lot sizing, negative prices, total unimodularity

For integer activities, conditioning on the support makes a fixed-charge objective affine. If every support-conditioned cell is integral, an optimal solution is a vertex of its cell for arbitrary fixed charges and marginal rates. A totally unimodular constraint matrix with integral data guarantees this condition. This surviving property is weaker than the classical conclusions. A … Read more