Month: May 2026

Normalized stochastic proximal approximation methods for nonsmooth composite optimization under heavy-tailed noise

  • Chunhao Han
  • Xiao Wang
  • Pengxiang Xu
  • Jin Zhang
    • Categories Nonlinear Optimization, Nonsmooth Optimization

    In this paper, we study nonsmooth composite optimization problems under heavy-tailed noise, with the objective being a summation of a nested function and a nonsmooth convex regularizer. We propose stochastic proximal approximation methods incorporating a normalization technique to handle the potential challenges caused by the nonsmooth regularizer and heavy-tailed noise. For the case where the … Read more

    Function-free Optimization via Comparison Oracles

  • Katya Scheinberg
  • Zikai Xiong
    • Categories Convex Optimization, Nonlinear Optimization Tags , , ,

    In this work, we study optimization specified only through a comparison oracle: given two points, it reports which one is preferred. We call it function-free optimization because we do not assume access to, nor the existence of, a canonical application-given objective function. Instead, our goal is to find a most-preferred feasible point, which we call … Read more

    Optimality Gap of Tailored Base-Surge Policies Decays Exponentially in Regular-Source Lead Times for Dual-Sourcing Models

  • Xin Chen
  • Shuai Li
  • Weijun Xie
    • Categories Dynamic Programming, Stochastic Programming, Supply Chain Management Tags , , , , ,

    This paper resolves an open problem posed in the literature by proving that, in dual-sourcing inventory systems, the optimality gap of tailored base-surge (TBS) policies decays exponentially with the regular source lead time, with the express-source lead time fixed. In contrast to the existing approach, which relies on conditional Jensen inequalities and a vanishing-discount argument … Read more

    Inexact Cubic Regularization Method with Adaptive Reuse of Hessian Approximations

  • Max L. N. Gonçalves
  • Vilmar Gehlen Filho
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    This work introduces an inexact cubic regularization method with adaptive reuse of Hessian approximations to solve general non-convex optimization problems. In the proposed approach, the gradient is computed inexactly and updated at every iteration, whereas the Hessian approximation is updated at a specific iteration and then reused for $m$ subsequent iterations (a lazy strategy), where … Read more

    Stochastic block coordinate and function alternation for multi-objective optimization and learning

  • Trang H. Tran
  • Luis Nunes Vicente
    • Categories Multi-Criteria Optimization Tags , , ,

    Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step, such methods require computing gradients with respect to all variables at every iteration, resulting in high computational costs in large-scale settings. In this work, we … Read more

    Betweenness Central Nodes Under Uncertainty: An Absorbing Markov Chain Approach

  • Wencheng Bao
  • Eleftheria Kontou
  • Chrysafis Vogiatzis
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Robust Optimization Tags , , , , , , ,

    We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This … Read more

    Accuracy and Relationships of Quadratic Models in Derivative-free Optimization

  • Yiwen Chen
  • Warren Hare
  • Lindon Roberts
    • Categories Nonlinear Optimization Tags , ,

    We study three quadratic models in model-based derivative-free optimization: the minimum norm (MN), minimum Frobenius norm (MFN), and quadratic generalized simplex derivative (QS) models. Despite their widespread use, their approximation accuracy and relationships have not been systematically explored. We establish fully linear error bounds for all three models, removing the uniformly bounded model Hessian assumption … Read more

    Inexact proximal point method for piecewise-star-convex function

  • Orizon Pereira Ferreira
  • Max L. N. Gonçalves
  • Jefferson Gonçalves Melo
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We propose and analyze an inexact proximal point method for minimizing locally Lipschitz functions on Euclidean spaces with a piecewise star-convex structure. More precisely, the space is covered by finitely many closed convex sets, and on each set the objective function satisfies a star-convex inequality with respect to the minimizers of its restriction. This class … Read more

    Storage Participation in Electricity Markets: Time Discretization through Robust Optimization

  • Dirk Lauinger
  • Xu Andy Sun
    • Categories Energy, Global Optimization, Robust Optimization Tags , , , ,

    Electricity storage is used for intertemporal price arbitrage and for ancillary services that balance unforeseen supply and demand fluctuations via frequency regulation. We present an optimization model that computes bids for both arbitrage and frequency regulation and ensures that storage operators can honor their market commitments at all times for all fluctuation signals in an … Read more

    A Binary Search-Based Criterion Space Algorithm for Solving Bi-Objective Integer Programs: The Quadtree Search Method

  • Lagnajita Basu
  • Aadya Bhattarai
  • Tapas Das
  • Kimia Keshanian
  • Hadi Charkhgard
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , , ,

    We propose an exact binary search-based branch-and-bound algorithm, termed the Quadtree Search Method, for solving bi-objective integer programs. The existing literature on criterion space search methods for multi-objective optimization predominantly assumes that subproblems can be solved to optimality, an assumption that becomes computationally prohibitive for hard instances. In contrast, our approach departs from this assumption … Read more