Month: July 2025

On the Convergence and Complexity of Proximal Gradient and Accelerated Proximal Gradient Methods under Adaptive Gradient Estimation

  • Raghu Bollapragada
  • Shagun Gupta
    • Categories Nonlinear Optimization, Optimization in Data Science, Stochastic Programming Tags , , , ,

    In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We consider settings where the smooth component is either a finite-sum function or an expectation of a stochastic function, … Read more

    Faster stochastic cubic regularized Newton methods with momentum

  • Yiming Yang
    • Categories Nonlinear Optimization, Optimization in Data Science, Unconstrained Optimization Tags , , ,

    Cubic regularized Newton (CRN) methods have attracted significant research interest because they offer stronger solution guarantees and lower iteration complexity. With the rise of the big-data era, there is growing interest in developing stochastic cubic regularized Newton (SCRN) methods that do not require exact gradient and Hessian evaluations. In this paper, we propose faster SCRN … Read more

    Sub-sampled Trust-Region Methods with Deterministic Worst-Case Complexity Guarantees

  • Max L. N. Gonçalves
  • Geovani Nunes Grapiglia
    • Categories Unconstrained Optimization Tags , , ,

    In this paper, we develop and analyze sub-sampled trust-region methods for solving finite-sum optimization problems. These methods employ subsampling strategies to approximate the gradient and Hessian of the objective function, significantly reducing the overall computational cost. We propose a novel adaptive procedure for deterministically adjusting the sample size used for gradient (or gradient and Hessian) … Read more

    The complete edge relaxation for binary polynomial optimization

  • Alberto Del Pia
  • Aida Khajavirad
    • Categories 0-1 Programming, Global Optimization, Integer Programming Tags , , , , ,

    We consider the multilinear polytope defined as the convex hull of the feasible region of a linearized binary polynomial optimization problem. We define a relaxation in an extended space for this polytope, which we refer to as the complete edge relaxation. The complete edge relaxation is stronger than several well-known relaxations of the multilinear polytope, … Read more

    Stochastic Approximation with Block Coordinate Optimal Stepsizes

  • Tao Jiang
  • Lin Xiao
    • Categories Data Science Algorithms, Optimization in Data Science Tags , ,

    We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an optimal point. These stepsize rules employ online estimates of the second moment of the search direction along each block coordinate. The popular Adam algorithm can be interpreted as a particular … Read more

    Anesthesiologist Scheduling with Handoffs: A Combined Approach of Optimization and Human Factors

  • Ankit Bansal
  • Osman Y. Ozaltin
    • Categories Integer Programming, Scheduling, Stochastic Programming

    We present a two-stage stochastic programming model for optimizing anesthesiologist schedules, explicitly accounting for uncertainty in surgery durations and anesthesiologist handoffs. To inform model design, we conducted an online survey at our partner institution to identify key factors affecting the quality of intraoperative anesthesiologist handoffs. Insights from the survey results are incorporated into the model, … Read more

    Non-smooth stochastic gradient descent using smoothing functions

  • Tommaso Giovannelli
  • Jingfu Tan
  • Luis Nunes Vicente
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with the non-differentiability of the outer function, we approximate the original non-smooth function using smoothing functions, which are continuously differentiable and approach … Read more

    Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization

  • Serge Gratton
  • Alena Kopanicakova
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Data Science Algorithms, Nonlinear Optimization Tags , , , , , ,

    Two OFFO (Objective-Function Free Optimization) noise tolerant algorithms are presented that handle bound constraints, inexact gradients and use second-order information when available. The first is a multi-level method exploiting a hierarchical description of the problem and the second is a domain-decomposition method covering the standard addditive Schwarz decompositions. Both are generalizations of the first-order AdaGrad … Read more

    Optimal personnel scheduling in hospital pharmacies considering management and operators priorities

  • Eduardo Souza
  • Walton P. Coutinho
  • Luciano Costa
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Scheduling Tags , ,

    In this paper, we address the problem of allocating and scheduling employees for work shifts in the pharmacy sector of a private hospital. To tackle this issue, we introduce the pharmacy staff scheduling problem (PSSP) in the literature. To solve the problem, we propose a mixed-integer programming formulation that considers various aspects, such as the … Read more

    On the Structure of the Inverse-Feasible Region of a Multiobjective Integer Program

  • Tyler Perini
    • Categories Combinatorial Optimization, Integer Programming, Multi-Criteria Optimization Tags , ,

    Many optimization problems are made more challenging due to multiple, conflicting criteria. The subjective nature of balancing these criteria motivates techniques for inverse optimization. This study establishes foundations for an exact representation of the inverse feasible region of a multiobjective integer program. We provide the first insights into its exact structure, as well as two … Read more