Machine Learning Algorithms for Improving Black Box Optimization Solvers

  • Morteza Kimiaei
  • Vyacheslav Kungurtsev
    • Categories Global Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , , ,

    Black-box optimization (BBO) addresses problems where objectives are accessible only through costly queries without gradients or explicit structure. Classical derivative-free methods—line search, direct search, and model-based solvers such as Bayesian optimization—form the backbone of BBO, yet often struggle in high-dimensional, noisy, or mixed-integer settings. Recent advances use machine learning (ML) and reinforcement learning (RL) to … Read more

    Sequential test sampling for stochastic derivative-free optimization

  • Anjie Ding
  • Francesco Rinaldi
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , ,

    In many derivative-free optimization algorithms, a sufficient decrease condition decides whether to accept a trial step in each iteration. This condition typically requires that the potential objective function value decrease of the trial step, i.e., the true reduction in the objective function value that would be achieved by moving from the current point to the … Read more

    New insights and algorithms for optimal diagonal preconditioning

  • Saeed Ghadimi
  • Woosuk L. Jung
  • Arnesh Sujanani
  • David Torregrosa-Belén
  • Henry Wolkowicz
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization, Optimization in Data Science Tags , , , ,

    Preconditioning (scaling) is essential in many areas of mathematics, and in particular in optimization. In this work, we study the problem of finding an optimal diagonal preconditioner. We focus on minimizing two different notions of condition number: the classical, worst-case type, \(\kappa\)-condition number, and the more averaging motivated \(\omega\)-condition number. We provide affine based pseudoconvex … Read more

    A linearly convergent algorithm for variational inequalities based on fiber bundle

  • Hongbo Sun
    • Categories Complementarity and Variational Inequalities, Game Theory Tags , , ,

    The variational inequality (VI) problem is a fundamental mathematical framework for many classical problems. This paper introduces an algorithm that applies to arbitrary finite-dimensional VIs with general compact convex sets and general continuous functions. The algorithm guarantees global linear convergence to an approximate solution without requiring any assumptions, including the typical monotonicity. Our approach adapts … Read more

    MDP modeling for multi-stage stochastic programs

  • David P. Morton
  • Oscar Dowson
  • Bernardo K. Pagnoncelli
    • Categories Stochastic Programming Tags , , , ,

    We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous state and action spaces. We extend policy graphs to include decision-dependent uncertainty for one-step transition probabilities as well as a limited form of statistical learning. We focus on the expressiveness of … Read more

    An extension of an interior-point method to include risk aversion in large-scale multistage stochastic optimization

  • Jordi Castro
  • Laureano F. Escudero
  • Juan F. Monge
    • Categories Linear Programming, Stochastic Programming Tags , , , ,

    In the earlier paper “On solving large-scale multistage stochastic optimization problems with a new specialized interior-point approach, European Journal of Operational Research, 310 (2023), 268–285” the authors presented a novel approach based on a specialized interior-point method (IPM) for solving (risk neutral) large-scale multistage stochastic optimization problems. The method computed the Newton direction by combining … Read more

    Approximating value functions via corner Benders’ cuts

  • Matheus Jun Ota
  • Ricardo Fukasawa
  • Aleksandr M. Kazachkov
    • Categories Branch and Cut Algorithms, Integer Programming, Stochastic Programming Tags , , , , ,

    We introduce a novel technique to generate Benders’ cuts from a conic relaxation (“corner”) derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining inequalities for the epigraph associated to this corner, we develop a computationally-efficient algorithm based on a compact reverse polar formulation … Read more

    Approximating inequality systems within probability functions: studying implications for problems and consistency of first-order information

  • Wim van Ackooij
  • Pedro Pérez-Aros
  • David Villacís
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , , ,

    In this work, we are concerned with the study of optimization problems featuring so-called probability or chance constraints. Probability constraints measure the level of satisfaction of an underlying random inequality system and ensure that this level is high enough. Such an underlying inequality system could be expressed by an abstractly known or perhaps costly to … Read more

    Drone Station Location and Routing Optimization for Infrastructure Inspection

  • Chun Cheng
    • Categories Transportation Tags , , , ,

    Recent advancements in drone technology have expanded drone applications in logistics, humanitarian aid, and infrastructure surveillance. Motivated by the demand for drone-based infrastructure inspection and the emerging design of drone battery swapping stations, this paper introduces the location routing problem with heterogeneous stations and drones (LRPHSD). In the problem, two types of stations are considered: … Read more

    Solution of Stochastic Facility Location Problems with Combinatorially many Decision-Dependent Distributions

  • Giovanni Pantuso
    • Categories Combinatorial Optimization, Facility Planning and Design, Stochastic Programming

    This article describes a model and an exact solution method for facility location problems with decision-dependent uncertainties. The model allows characterizing the probability distribution of the random elements as a function of the choice of open facilities. This, in turn, generates a combinatorial number of potential distributions of the random elements. Though general in the … Read more