Smoothing fast iterative hard thresholding algorithm for $\ell_0$ regularized nonsmooth convex regression problem

  • Wei Bian
  • Fan Wu
  • Xiaoping Xue
    • Categories Nonlinear Optimization Tags , , , , ,

    We investigate a class of constrained sparse regression problem with cardinality penalty, where the feasible set is defined by box constraint, and the loss function is convex, but not necessarily smooth. First, we put forward a smoothing fast iterative hard thresholding (SFIHT) algorithm for solving such optimization problems, which combines smoothing approximations, extrapolation techniques and … Read more

    A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds

  • Xiaojun Chen
  • Shiqian Ma
  • Chao Zhang
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper, we propose a Riemannian smoothing steepest descent method to minimize a nonconvex and non-Lipschitz function on submanifolds. The generalized subdifferentials on Riemannian manifold and the Riemannian gradient sub-consistency are defined and discussed. We prove that any accumulation point of the sequence generated by the Riemannian smoothing steepest descent method is a stationary … Read more

    On Convex Lower-Level Black-Box Constraints in Bilevel Optimization with an Application to Gas Market Models with Chance Constraints

  • Holger Heitsch
  • René Henrion
  • Thomas Kleinert
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Cutting Plane Approaches, Stochastic Programming Tags , , , ,

    Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this … Read more

    One-dimensional multi-period cutting stock problems in the concrete industry

  • Silvio Alexandre de Araujo
  • Caroline de Arruda Signorini
  • Gislaine Mara Melega
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Combinatorial Optimization

    This research looks at the production planning of hollow-core slabs integrated to the optimization problem of the use of molds. Considering the production process of these structures, two mathematical models are proposed for the arising problem, which consists of a one-dimensional multi-period cutting stock problem with innovative aspects regarding the multiple manufacturing modes that can … Read more

    Hölder Gradient Descent and Adaptive Regularization Methods in Banach Spaces for First-Order Points

  • Serge Gratton
  • Philippe L. Toint
  • Sadok Jerad
    • Categories Unconstrained Optimization Tags , ,

    This paper considers optimization of smooth nonconvex functionals in smooth infinite dimensional spaces. A Hölder gradient descent algorithm is first proposed for finding approximate first-order points of regularized polynomial functionals. This method is then applied to analyze the evaluation complexity of an adaptive regularization method which searches for approximate first-order points of functionals with $\beta$-H\”older … Read more

    Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients

  • Ernesto G. Birgin
  • José Mario Martínez
    • Categories Nonlinear Systems and Least-Squares Tags , , ,

    A general framework for solving nonlinear least squares problems without the employment of derivatives is proposed in the present paper together with a new general global convergence theory. With the aim to cope with the case in which the number of variables is big (for the standards of derivative-free optimization), two dimension-reduction procedures are introduced. … Read more

    The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case

  • Stefania Bellavia
  • Gianmarco Gurioli
  • Benedetta Morini
  • Philippe L. Toint
    • Categories Unconstrained Optimization Tags , , ,

    Intrinsic noise in objective function and derivatives evaluations may cause premature termination of optimization algorithms. Evaluation complexity bounds taking this situation into account are presented in the framework of a deterministic trust-region method. The results show that the presence of intrinsic noise may dominate these bounds, in contrast with what is known for methods in … Read more

    Hospital-wide Inpatient Flow Optimization

  • Dimitris Bertsimas
  • Jean Pauphilet
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    An ideal that supports quality and delivery of care is to have hospital operations that are coordinated and optimized across all services in real-time. As a step toward this goal, we propose a multistage adaptive robust optimization approach combined with machine learning techniques. Informed by data and predictions, our framework unifies the bed assignment process … Read more

    The Integrated Lot Sizing and Cutting Stock Problem in an Automotive Spring Factory

  • Pedro Rochavetz de Lara Andrade
  • Adriana Cristina Cherri
  • Silvio Alexandre de Araujo
  • Felipe Kesrouani Lemos
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Combinatorial Optimization

    In this paper, a manufacturer of automotive springs is studied in order to reduce inventory costs and losses in the steel bar cutting process. For that, a mathematical model is proposed, focused on the short term decisions of the company, and considering parallel machines and operational constraints, besides the demand, inventory costs and limits for … Read more

    Integrated lot-sizing and one-dimensional cutting stock problem with usable leftovers

  • Adriana Cristina Cherri
  • Silvio Alexandre de Araujo
  • D. N. do Nascimento
    • Categories Linear Programming

    This paper addresses the integration of the lot-sizing problem and the one-dimensional cutting stock problem with usable leftovers (LSP-CSPUL). This integration aims to minimize the cost of cutting items from objects available in stock, allowing the bringing forward production of items that have known demands in a future planning horizon. The generation of leftovers, that … Read more