Applications – Science and Engineering

Adaptive regularization algorithms with inexact evaluations for nonconvex optimization

  • Stefania Bellavia
  • Benedetta Morini
  • Philippe L. Toint
  • Gianmarco Gurioli
    • Categories Constrained Nonlinear Optimization, Data-Mining, Unconstrained Optimization Tags , , , ,

    A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constraints whose evaluation and enforcement has negligible cost) under the assumption that the derivative of highest degree is beta-H\”{o}lder continuous. It features a … Read more

    A Unified Framework for Sparse Relaxed Regularized Regression: SR3

  • Aleksandr Y. Aravkin
  • Peng Zheng
  • Travis Askham
  • Steve Brunton
  • Nathan Kutz
    • Categories Nonlinear Systems and Least-Squares, Nonsmooth Optimization, Statistics Tags , , , ,

    Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, vari- able selection, and high-dimensional analysis. We propose a broad framework for sparse relaxed regularized regression, called SR3. The key idea is to solve a relaxation of … Read more

    Strong mixed-integer programming formulations for trained neural networks

  • Ross Anderson
  • Joey Huchette
  • Juan Pablo Vielma
  • Will Ma
  • Christian Tjandraatmadja
    • Categories (Mixed) Integer Linear Programming, Statistics Tags , ,

    We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying that an image classification network is robust to adversarial inputs, or solving decision problems where the objective function is a machine learning model. … Read more

    Nonmonotonicity and Quasiconvexity on Equilibrium Problems

  • Lennin Mallma Ramirez
    • Categories Applications - Science and Engineering, Complementarity and Variational Inequalities, Nonsmooth Optimization

    In this note, some results are introduced considering the assumptions of quasiconvexity and nonmonotonicity, finally an application and an idea to solve the quasiconvex equilibrium problem are presented considering these new results. Article Download View Nonmonotonicity and Quasiconvexity on Equilibrium Problems

    Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Data-Mining, Nonlinear Systems and Least-Squares Tags , , , , ,

    We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected) constraints, if any, is negligible compared to that of evaluating the objective function. These bounds unify, extend or improve all known upper and lower complexity bounds … Read more

    n-step cutset inequalities: facets for multi-module capacitated network design problem

  • Kiavash Kianfar
  • Haochen Luo
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Facility Planning and Design

    Many real-world decision-making problems can be modeled as network design problems, especially on networks with capacity requirements on links. In network design problems, decisions are made on installation of flow transfer capacities on the links and routing of flow from a set of source nodes to a set of sink nodes through the links. Many … Read more

    Towards Resilient Operation of Multi-Microgrids: An MISOCP-Based Frequency-Constrained Approach

  • Amin Gholami
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Control Applications, Energy Tags , , , , ,

    High penetration of distributed energy resources (DERs) is transforming the paradigm in power system operation. The ability to provide electricity to customers while the main grid is disrupted has introduced the concept of microgrids with many challenges and opportunities. Emergency control of dangerous transients caused by the transition between the grid-connected and island modes in … Read more

    Data-Driven Maintenance and Operations Scheduling in Power Systems under Decision-Dependent Uncertainty

  • Shabbir Ahmed
  • Nagi Gebraeel
  • Beste Basciftci
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering Tags , , ,

    Generator maintenance scheduling plays a pivotal role in ensuring uncompromising operations of power systems. There exists a tight coupling between the condition of the generators and corresponding operational schedules, significantly affecting reliability of the system. In this study, we effectively model and solve an integrated condition-based maintenance and operations scheduling problem for a fleet of … Read more

    On tradeoffs between treatment time and plan quality of volumetric-modulated arc therapy with sliding-window delivery

  • Lovisa Engberg
  • Anders Forsgren
    • Categories Applications - Science and Engineering Tags , , ,

    The purpose of this study is to give an exact formulation of optimization of volumetric-modulated arc therapy (VMAT) with sliding-window delivery, and to investigate the plan quality effects of decreasing the number of sliding-window sweeps made on the 360-degree arc for a faster VMAT treatment. In light of the exact formulation, we interpret an algorithm … Read more

    Global Convergence in Deep Learning with Variable Splitting via the Kurdyka-{\L}ojasiewicz Property

  • T Lau
  • S Lin
  • S Ouyang
  • Y Yuan
  • Jinshan Zeng
    • Categories Convex and Nonsmooth Optimization, Data-Mining Tags , , ,

    Deep learning has recently attracted a significant amount of attention due to its great empirical success. However, the effectiveness in training deep neural networks (DNNs) remains a mystery in the associated nonconvex optimizations. In this paper, we aim to provide some theoretical understanding on such optimization problems. In particular, the Kurdyka-{\L}ojasiewicz (KL) property is established … Read more