Robust Network Design for Potential-Based Flows with Controllable Elements

  • Kristina Rolsing
  • Johannes Thürauf
    • Categories (Mixed) Integer Nonlinear Programming, Bilevel Optimization, Robust Optimization Tags , , , ,

    We study adjustable robust network design for potential-based flows with controllable elements under load uncertainty. The resulting problem combines discrete here-and-now expansion decisions with wait-and-see operational decisions governed by nonconvex flow constraints. Moreover, controllable elements introduce adjustable integer decisions, which are algorithmically challenging. We equivalently characterize robust feasibility and robust optimality of a fixed network … Read more

    D-optimal partitioning: design of experiments under heterogeneous treatment effects

  • Jiaqi Wang
  • Weijun Xie
    • Categories Combinatorial Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

    Modern experimentation in business and public policy often studies targeted interventions whose effects depend on the heterogeneous attributes of individuals. We examine heterogeneous treatment effects through the lens of optimal design of experiments, which allocates treatment decisions to maximize the precision of estimated treatment-covariate interactions. We introduce the D-optimal partitioning problem for balancing the information … Read more

    PyROS: The Pyomo Robust Optimization Solver

  • Jason A. F. Sherman
  • Natalie M. Isenberg
  • John D. Siirola
  • Chrysanthos E. Gounaris
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems, Robust Optimization Tags , , , ,

    We present PyROS, a Python-based meta-solver that automates a generalized cutting-set algorithm for the solution of nonconvex two-stage robust optimization (RO) problems with uncertain equality constraints. Freely available through the open-source optimization software package Pyomo, PyROS is designed to operate on a user-provided deterministic model and uncertainty set, such that a solution to the RO … Read more

    On exact copositive representation of simplicial quadratic optimization problems, their strong conic duality and a new proof of the Frank-Wolfe theorem

  • Immanuel M. Bomze
  • E. Alper Yildirim
    • Categories Cone Programming, Global Optimization, Global Optimization Theory

    We are interested in exactness, strong conic duality and dual attainability in copositive relaxations of quadratic optimization problems (QPs) of a special form, in which any (feasible) QP can be recast. By using our results, the celebrated Frank-Wolfe theorem on the attainability of any bounded QP even over unbounded polyhedra, regardless of whether the objective … Read more

    When do Mixed-Integer Games Admit Rational Equilibria?

  • Alois Duguet
  • Tobias Harks
  • Martin Schmidt
  • Julian Schwarz
    • Categories (Mixed) Integer Linear Programming, Game Theory Tags , , , ,

    We consider mixed-integer linear-quadratic generalized Nash equilibrium problems, i.e., games in which each player solves a mixed-integer program subject to linear constraints in her own and rivals’ strategies as well as an objective which is quadratic in her own strategies and bilinear in her own and rivals’ strategies. For this class of games, we study … Read more

    Automorphisms of hyperbolic polynomials

  • Michael Orlitzky
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    The pair \( (p,e) \) is hyperbolic if \( p : \mathbb{R}^{n} \to \mathbb{R} \) is a homogeneous polynomial, if \( e \in \mathbb{R}^{n} \), if \( p(e) > 0 \), and if the roots of \( t \mapsto p(te – x) \) are real for all \( x \in \mathbb{R}^{n} \). In that case, … Read more

    Distributionally Robust Optimization with General Uncertainty Structure

  • Judith Brugman
  • Dimitris Bertsimas
  • Johan Van Leeuwaarden
  • Dick den Hertog
    • Categories Nonlinear Optimization, Robust Optimization, Stochastic Programming Tags , , , , , ,

    We develop an exact solution framework for a broad class of Distributionally Robust Optimization (DRO) problems with general uncertainty structure. Within the class of moment- and confidence-set-based ambiguity sets, existing exact methods are largely limited to max-of-affine functions under ambiguity sets with strictly nested confidence sets. To enlarge this scope while preserving tractability, we introduce … Read more

    Optimization Reformulations of Complementarity Equilibrium Models

  • Laura Bahiense
  • Marcelo Cordova
  • Juan Pablo Luna
  • Claudia Sagastizábal
    • Categories Applications - Science and Engineering, Complementarity and Variational Inequalities, Energy Tags , ,

    We propose a new mathematical model to describe equilibria in competitive markets. Our approach transforms the well-known complementary formulation into a numerically more efficient optimization framework. In complementarity models, the actions of all elastic consumers in the market are implicitly represented by their aggregate demand. Instead, we introduce demand-induced utilities, which can be explicitly constructed individually for each consumer. … Read more

    Stage-wise hybrid nested Benders’ decomposition-stochastic dual dynamic programming for virtual power plants

  • Youngdoo Choi
  • Seokwoo Kim
  • Sanghyeon Bae
  • Dong Gu Choi
    • Categories Dynamic Programming, Energy, Stochastic Programming Tags , , ,

    Participants in energy markets make sequential decisions across multiple time horizons under uncertainty, leading to large-scale multistage stochastic optimization problems. Stochastic dual dynamic programming is widely used for its tractability, but its application to modern energy markets is challenged by nested dependencies induced by participation across multiple interrelated markets under increasing uncertainty from distributed energy … Read more

    Advancing Branch-and-Price for Graph Coloring: New Pricing Strategies and Benchmark Results

  • Mingming Zheng
  • Roberto Baldacci
  • Fabio Furini
  • Qinghua Wu
    • Categories 0-1 Programming, Combinatorial Optimization, Integer Programming Tags , , ,

    This paper proposes BPCOL+, an exact branch-and-price algorithm for the Graph Coloring Problem. The algorithm is both novel and highly effective, integrating enhanced pricing strategies within Zero-Suppressed Binary Decision Diagrams (ZDDs) to efficiently solve the pricing problem associated with the maximal-stable-set-based set-covering formulation. After computing upper and lower bounds at the root node using heuristic … Read more