Bregman Regularized Proximal Point Methods for Computing Projected Solutions of Quasi-equilibrium Problems

  • Richard Osward
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonlinear Optimization Tags , , ,

    In this paper, we propose two Bregman regularized proximal point methods that provide flexibility to compute projected solutions for quasi-equilibrium problems. Each method has one Bregman projection onto the feasible set and the regularized equilibrium problem. Under standard assumptions, we prove that the methods are well-defined and that the sequences they generate converge to a … Read more

    Modeling Adversarial Wildfires for Power Grid Disruption

  • Matthew Brun
  • Xu Andy Sun
  • Jean-Paul Watson
    • Categories (Mixed) Integer Nonlinear Programming, Energy, Second-Order Cone Programming Tags , , , ,

    Electric power infrastructure faces increasing risk of damage and disruption due to wildfire. Operators of power grids in wildfire-prone regions must consider the potential impacts of unpredictable fires. However, traditional wildfire models do not effectively describe worst-case, or even high-impact, fire behavior. To address this issue, we propose a mixed-integer conic program to characterize an … Read more

    A Newsvendor Model for Last-Mile Fleet Sizing

  • Benjamin Rojas
  • Homero Larrain
  • Mathias A. Klapp
  • Dipayan Banerjee
    • Categories Applications - OR and Management Sciences, Production and Logistics, Transportation Tags , , ,

    We study the tactical problem of determining a last-mile delivery fleet size while accounting for day-to-day uncertainty in the number and location of customer requests. An optimally sized fleet must balance the cost of contracting vehicles against the penalty costs of unserved customers: a larger fleet reduces the risk of unserved demand, but a smaller … Read more

    Finding Minimal Discretizations in Dynamic Discretization Discovery for Continuous-Time Service Network Design

  • Tom Wüllner
  • Alexander Helber
    • Categories Combinatorial Optimization, Network Optimization, Transportation Tags , , ,

    The dynamic discretization discovery framework is a powerful tool for solving network design problems with a temporal component by iteratively refining a time-discretized model. Existing approaches refine the time discretization in ways that guarantee eventual termination. However, refinement choices are not unique, and better choices can yield smaller and easier-to-solve time-discretized models. We pose the … Read more

    Normal cones and subdifferentials at infinity for convex analysis and optimization

  • Thanh-Hung Pham
    • Categories Convex Optimization Tags , , ,

    Motivated by recent developments, this paper further investigates normal cones and subdifferentials at infinity within the framework of convex analysis. We establish fundamental properties of these constructions and derive basic calculus rules. The obtained results extend and refine existing concepts in variational analysis and nonsmooth optimization, providing new insights into the asymptotic structure of functions … Read more

    Compact Lifted Relaxations for Low-Rank Optimization

  • Ryan Cory-Wright
  • Jean Pauphilet
    • Categories Semi-definite Programming Tags , ,

    We develop tractable convex relaxations for rank-constrained quadratic optimization problems over nxm matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral structure. We derive lifted semidefinite relaxations that do not require such spectral terms. Although a direct lifting introduces a large semidefinite constraint in dimension n2 … Read more

    Data-driven Policies For Two-stage Stochastic Linear Programs

  • Chhavi Sharma
  • Harsha Gangammanavar
    • Categories Linear Programming, Optimization in Data Science, Stochastic Programming Tags , , ,

    A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes. However, in practical applications, quick decision-making is necessary, and solving a stochastic program from scratch for every change in input data can be computationally costly. This … Read more

    Preconditioned Proximal Gradient Methods with Conjugate Momentum: A Subspace Perspective

  • Jian Chen
  • Xinmin Yang
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , ,

    In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned proximal subproblem admits a closed-form solution through its dual formulation. However, such a structure-driven preconditioner may be poorly aligned with the local curvature … Read more

    Strong convergence, perturbation resilience and superiorization of Generalized Modular String-Averaging with infinitely many input operators

  • Kay Barshad
  • Yair Censor
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , ,

    We study the strong convergence and bounded perturbation resilience of iterative algorithms based on the Generalized Modular String-Averaging (GMSA) procedure for infinite sequences of input operators under a general admissible control. These methods address a variety of feasibility-seeking problems in real Hilbert spaces, including the common fixed point problem and the convex feasibility problem. In … Read more

    Optimal Transport on Lie Group Orbits

  • Bahar Taskesen
    • Categories Infinite Dimensional Optimization, Other Topics

    In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and formalize it using Lie group theory. Fixing a Lie group action on the outcome space and a reference distribution, we study optimal transport … Read more