Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs

  • E. Alper Yildirim
    • Categories Global Optimization, Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , , ,

    We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation). By incorporating the first-order optimality conditions, a quadratic program can be formulated as an optimization problem with complementarity constraints. We investigate the effect of incorporating optimality … Read more

    SDP bounds on the stability number via ADMM and intermediate levels of the Lasserre hierarchy

  • Lennart Sinjorgo
  • Renata Sotirov
  • Juan C. Vera
    • Categories Combinatorial Optimization, Semi-definite Programming Tags , , ,

    We consider the Lasserre hierarchy for computing bounds on the stability number of graphs. The semidefinite programs (SDPs) arising from this hierarchy involve large matrix variables and many linear constraints, which makes them difficult to solve using interior-point methods. We propose solving these SDPs using the alternating direction method of multipliers (ADMM). When the second … Read more

    On Local Search in Bilevel Mixed-Integer Linear Programming

  • Eneko C. Clemente
  • Oleg A. Prokopyev
    • Categories Bilevel Optimization, Game Theory, Other Topics Tags , ,

    Two-level hierarchical decision-making problems, where a leader’s choice influences a follower’s action, arise across key business and public-sector domains, from market design and pricing to defense. These problems are typically modeled as bilevel programs and are known to be notoriously hard to solve at scale. In single-level combinatorial optimization, especially for challenging instances, local search … Read more

    Statistical Inference for Distributed Contextual Multi-armed Bandit

  • Wuwenqing Yan
  • Yongchao Liu
    • Categories Stochastic Programming Tags , , , ,

    In this paper, we study the online statistical inference of distributed contextual multi-armed bandit problems, where the agents collaboratively learn an optimal policy by exchanging their local estimates of the global parameters with neighbors over a communication network. We propose a distributed online decision making algorithm, which balances the exploration and exploitation dilemma via the … Read more

    Asymptotically Fair and Truthful Allocation of Public Goods

  • Arnesh Sujanani
    • Categories Convex and Nonsmooth Optimization, Game Theory, Nonlinear Optimization Tags , , ,

    We study the fair and truthful allocation of m divisible public items among n agents, each with distinct preferences for the items. To aggregate agents’ preferences fairly, we focus on finding a core solution. For divisible items, a core solution always exists and can be calculated by maximizing the Nash welfare objective. However, such a … Read more

    A relax-fix-and-exclude algorithm for an MINLP problem with multilinear interpolations

  • Bruno Machado Pacheco
  • Laio Seman
    • Categories (Mixed) Integer Nonlinear Programming, Chemical Engineering, Global Optimization Applications Tags , ,

    This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objectives or constraints contain black-box functions only known at a finite set of evaluations on a predefined grid. We derive a piecewise-linear relaxation for the multilinear interpolants, which require an MINLP formulation. Supported … Read more

    Two-way Cutting-plane Algorithm for Best Subset Selection Considering Multicollinearity

  • Yuichi Takano
    • Categories Global Optimization, Integer Programming, Optimization in Data Science Tags , , , ,

    When linear dependence exists between some explanatory variables in a regression model, the estimates of regression coefficients become unstable, thereby making the interpretation of the estimation results unreliable. To eliminate such multicollinearity, we propose a high-performance method for selecting the best subset of explanatory variables for linear and logistic regression models. Specifically, we first derive … Read more

    Lipschitz-Free Mirror Descent Methods for Non-Smooth Optimization Problems

  • Bowen Yuan
    • Categories Convex Optimization, Nonsmooth Optimization Tags , ,

    The part of the analysis of the convergence rate of the mirror descent method that is connected with the adaptive time-varying step size rules due to Alkousa et al. (MOTOR 2024, pp. 3-18) is corrected. Moreover, a Lipschitz-free mirror descent method that achieves weak ergodic convergence is presented, generalizing the convergence results of the mirror … Read more

    Interpretable SHAP-bounded Bayesian Optimization for Underwater Acoustic Metamaterial Coating Design

  • Elnaz Hajizadeh
    • Categories Civil and Environmental Engineering, Mechanical Engineering Tags , , , ,

    We developed an interpretability informed Bayesian optimization framework to optimize underwater acoustic coatings based on polyurethane elastomers with embedded metamaterial features. A data driven model was employed to analyze the relationship between acoustic performance, specifically sound absorption and the corresponding design variables. By leveraging SHapley Additive exPlanations (SHAP), a machine learning interpretability tool, we identified … Read more

    Constrained Bayesian Accelerated Design of Acoustic Polyurethane Coatings with Metamaterial Features Under Hydrostatic Pressure

  • Elnaz Hajizadeh
    • Categories Civil and Environmental Engineering, Mechanical Engineering Tags , , ,

    Here we propose a novel, fully automated framework for accelerated design of underwater acoustic coatings, targeting the reduction of acoustic signature of naval platforms under operational conditions, by coupling Bayesian Optimization (BO) with a 2-step Finite Element Model (FEM). The developed FEMs evaluate the acoustic performance of polyurethane (PU) coatings with embedded metamaterial features under … Read more