Robust Optimization

Contextual Distributionally Robust Optimization with Causal and Continuous Structure: An Interpretable and Tractable Approach

  • Jie Wang
    • Categories Optimization in Data Science, Robust Optimization, Stochastic Programming Tags ,

    In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules that prescribe decisions using covariates. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while … Read more

    A single loop method for quadratic minmax optimization

  • StefanoCipolla
  • Oliver Stein
  • Alain Zemkoho
    • Categories Linear Programming, Quadratic Programming, Robust Optimization Tags

    We consider a quadratic minmax problem with coupled inner constraints and propose a method to compute a class of stationary points. To motivate the need to compute such stationary points, we first show that they are meaningful, in the sense that they can be locally optimal for our problem under suitable linear independence and second-order … Read more

    A Gauge Set Framework for Flexible Robustness Design

  • Ningji Wei
  • Xian Yu
  • Peter Yun Zhang
    • Categories Robust Optimization, Stochastic Programming

    This paper proposes a unified framework for designing robustness in optimization under uncertainty using gauge sets, convex sets that generalize distance and capture how distributions may deviate from a nominal reference. Representing robustness through a gauge set reweighting formulation brings many classical robustness paradigms under a single convex-analytic perspective. The corresponding dual problem, the upper … Read more

    Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization

  • Jie Wang
    • Categories Infinite Dimensional Optimization, Optimization in Data Science, Robust Optimization

    Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized Wasserstein distance, referred to as Sinkhorn DRO. Existing work primarily addresses Sinkhorn DRO from a dual perspective, leveraging its formulation as a conditional stochastic optimization … Read more

    Robust optimality for nonsmooth mathematical programs with equilibrium constraints under data uncertainty

  • Vivek Laha
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization, Nonlinear Optimization, Nonsmooth Optimization, Robust Optimization Tags

    We develop a unified framework for robust nonsmooth optimization problems with equilibrium constraints (UNMPEC). As a foundation, we study a robust nonsmooth nonlinear program with uncertainty in both the objective function and the inequality constraints (UNP). Using Clarke subdifferentials, we establish Karush–Kuhn–Tucker (KKT)–type necessary optimality conditions under an extended no–nonzero–abnormal–multiplier constraint qualification (ENNAMCQ). When the … Read more

    Constraint Decomposition for Multi-Objective Instruction-Following in Large Language Models

  • Eva Paunova
    • Categories Applications - OR and Management Sciences, Robust Optimization

    Large language models (LLMs) trained with reinforcement learning from human feed- back (RLHF) struggle with complex instructions that bundle multiple, potentially con- icting requirements. We introduce constraint decomposition, a framework that separates multi-objective instructions into orthogonal componentssemantic correctness, structural organization, format specications, and meta-level requirementsand optimizes each in- dependently before hierarchical combination. Our approach addresses … Read more

    Robust combinatorial optimization problems under locally budgeted interdiction uncertainty against the objective function and covering constraints

  • Alejandro Crema
    • Categories Combinatorial Optimization, Robust Optimization Tags ,

    Recently robust combinatorial optimization problems with budgeted interdiction uncertainty affecting cardinality-based constraints or objective were considered by presenting, comparing and experimenting with compact formulations. In this paper we present a compact formulation for the case in which locally budgeted interdiction uncertainty affects the objective function and covering constraints simultaneously. ArticleDownload View PDF

    An alternating optimization approach for robust optimal control in chromatography

  • Dominik H. Cebulla
  • Andrea Gilch
  • Jan Hendrik Rolfes
  • Christian Kirches
  • Frauke Liers
    • Categories Optimization of Systems modeled by PDEs, Robust Optimization Tags , ,

    Chromatographic separation plays a vital role in various areas, as this technique can deliver high-quality products both in lab- and industrial-scale processes. Economical and also ecological benefits can be expected when optimizing such processes with mathematical methods. However, even small perturbations in the operating conditions can result in significantly altered results, which may lead to … Read more

    Integrated Planning of Drone-Based Disaster Relief: Facility Location, Inventory Prepositioning, and Fleet Operations under Uncertainty

  • Yuyang Ma
  • Karmel S. Shehadeh
  • Man Yiu Tsang
    • Categories Robust Optimization, Transportation

    We introduce a two-stage robust optimization (RO) framework for the integrated planning of a drone-based disaster relief operations problem (DDROP). Given sets of demand points, candidate locations for establishing drone-supported relief facilities, facility types, drone types, and relief items types, our first-stage problem solves the following problems simultaneously: (i) a location problem that determines the … Read more