Month: June 2026

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

    On the existence of Lagrange multipliers in conic programming

  • Gabriel Haeser
  • Daiana Santos
    • Categories Constrained Nonlinear Optimization Tags ,

    The existence of Lagrange multipliers at a solution of a nonlinear optimization problem constitutes one of the cornerstones of modern optimization theory, with many important consequences for guiding algorithmic procedures towards a solution, defining stopping criteria, performing stability analysis, and several other aspects. However, the proof of this result is often intricate, relying on non-trivial … Read more

    Scalable Finite Adaptability via Polyhedral Partition and Learning

  • Zolykha Rezaei
  • Ningji Wei
  • Eojin Han
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , ,

    We study finite adaptability for decision-making under uncertainty, where a small set of candidate solutions is prepared in advance and the best response is selected after uncertainty is realized. While existing methods have made significant progress on exact formulations, scalability remains a persistent challenge due to (i) the combinatorial nature of assigning decisions to uncertainty … Read more