Repository – Page 2 – Optimization Online

A Decision-Support Framework for Structuring and Reducing Large Multi-Objective Solution Sets via Clustering: An Application to Proton Therapy

Published: 2026/08/17

nicole

(Mixed) Integer Linear Programming, Biomedical Applications, Multi-Criteria Optimization clustering, decision support, extended goal programming, goal programming, intensity modulated proton therapy, multi-criteria decision analysis, multi-objective optimization, multiobjective optimization, OR for medicine, Pareto set reduction, radiotherapy treatment planning, representative selection.

This paper proposes a four-stage decision-support framework for structuring and reducing large multi-objective solution sets into compact and interpretable collections of representative alternatives. The methodology combines: (Phase 1) systematic solution generation through extended goal programming and structured preference exploration; (Phase 2) robustness-aware enrichment and profiling under weight sensitivity analysis; (Phase 3) filtering and dominance-based reduction … Read more

Congressional Apportionment

Published: 2026/08/17

(Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Integer Programming allocation problems, apportionment, MINLP, public sector operations

This book chapter is a gentle introduction to the mathematics of congressional apportionment. It emphasizes the connections between mathematical optimization and the classical apportionment methods (e.g., Jefferson, Adams, Hamilton, Webster, Huntington-Hill, Dean). CitationPrepared for a forthcoming book edited by Bruce Golden and Doug ShierArticleDownload View PDF

On the Absence of Identifiable Manifolds in Finite-Max Composite Optimization

Published: 2026/08/17

Nonlinear Optimization, Nonsmooth Optimization, Other Topics active manifolds, identifiable set, nonsmooth optimization

In nonsmooth optimization, identifiable sets describe the local region eventually reached by sequences converging to a prescribed critical point. When such a set is a \(C^2\) manifold on which the objective restricts to a \(C^2\) function, it is called an identifiable manifold. Their appeal lies in what they enable: many first-order methods identify these manifolds … Read more

Indicator Cuts for Benders Decomposition with Mixed-Integer Subproblems

Published: 2026/08/14

(Mixed) Integer Linear Programming, Energy, Polyhedra District energy system, generalized benders decomposition, Mixed-integer subproblem, non-convex cut formulation, Subproblem monotonicity

Classical Benders decomposition fails when the subproblem is a mixed-integer program, due to the absence of strong duality. We propose a novel class of dual-free indicator cuts that are applicable to all Benders-decomposable problems with a pure-integer master problem and mixed-integer linear programming (MILP) subproblems. These cuts are derived from the monotonicity property of the … Read more

A Shrinkage Path Heuristic for Wasserstein Distributionally Robust Optimization

Published: 2026/08/14

Robust Optimization, Stochastic Programming distributionally robust optimization, robust optimization, sample average approximation, wasserstein ambiguity

Wasserstein distributionally robust optimization (DRO) is a versatile and widely adopted framework for decision-making under uncertainty, yet its standard deterministic reformulations generally contain non-convex inner subproblems that are challenging to solve. To address this issue, we propose a shrinkage path heuristic that reduces the solution of a DRO problem to a one-dimensional search over the … Read more

Benders Decomposition with Partial Non-Anticipativity Relaxation for Multi-Stage Stochastic Clean Energy Transition Planning

Published: 2026/08/14

Stochastic Programming benders decomposition, clean energy transition, multi-stage stochastic programming, Non-anticipativity relaxation, or in energy

We study clean energy transition planning for campus-scale integrated electricity-heat systems under both strategic level and operational level uncertainties. We formulate a multi-stage stochastic mixed-integer program that jointly optimizes investment and operational decisions for renewable generation, storage, and heat-transfer technologies whose costs and efficiencies evolve stochastically across stages. To account for short-term operational uncertainty, we … Read more

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp

Published: 2026/08/12

Wenzhi Gao

Convex Optimization, Unconstrained Optimization

We revisit the Sinkhorn-Knopp (SK) algorithm for the matrix scaling problem. Despite extensive literature on the global convergence of SK and its variants, its local linear convergence behavior remains less understood. We address this gap by providing the first nonasymptotic local analysis of SK that matches the rate obtained from existing asymptotic Jacobian-based arguments. We … Read more

A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization

Published: 2026/08/12

Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science

For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher’s augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this paper, the analysis of this algorithm is extended, offering a two-fold contribution. First, it is shown that … Read more

Randomized block proximal method with locally Lipschitz continuous gradient

Published: 2026/08/11

Nonlinear Optimization large scale nonconvex optimization, local Lipschitz gradient continuity, nonnegative matrix factorization, proximal gradient algorithm, random block-coordinate descent algorithm

Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In this paper, we propose a randomized block proximal gradient algorithm for minimizing the sum of a smooth function and a separable proper lower semicontinuous function, both possibly … Read more

Online Performative Decision Making with Latent Distribution States

Published: 2026/08/11, Updated: 2026/08/13