Month: February 2021

A General Framework for Optimal Control of Fractional Nonlinear Delay Systems by Wavelets

  • Malmir Iman
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    An iterative procedure to find the optimal solutions of general fractional nonlinear delay systems with quadraticperformance indices is introduced. The derivatives of state equations are understood in the Caputo sense. By presenting and applying a general framework, we use the Chebyshev wavelet method developed for fractional linear optimal control to convert fractional nonlinear optimal control … Read more

    Path Planning and Network Optimization for UAV Swarms for Multi-Target Tracking

  • Shawon Dey
  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering

    This paper focuses on the development of decentralized collaborative sensing and sensor resource allocation algorithms where the sensors are located on-board autonomous unmanned aerial vehicles. We develop these algorithms in the context of single-target and multi-target tracking applications, where the objective is to maximize the tracking performance as measured by the mean-squared error between the … Read more

    A Comparative Study of Stability Representations for Solving Many-to-One Matching Problems with Utility-Weighted Objectives, Ties, and Incomplete Lists via Integer Optimization

  • Pitchaya Wiratchotisatian
  • Andrew C. Trapp
  • Hoda Atef Yekta
    • Categories Applications - OR and Management Sciences Tags , , , ,

    We consider integer optimization models for finding stable solutions to many-to-one, utility-weighted matching problems with incomplete preference lists and ties. While traditional algorithmic approaches for the stable many-to-one matching problem, such as the Deferred Acceptance algorithm, offer efficient performance for the strict problem setting, adaptation to alternative settings often requires careful customization. Optimization-based approaches are … Read more

    Beyond local optimality conditions: the case of maximizing a convex function

  • Aharon Ben-Tal
  • Ernst Roos
    • Categories Constrained Nonlinear Optimization, Global Optimization Tags , ,

    In this paper, we design an algorithm for maximizing a convex function over a convex feasible set. The algorithm consists of two phases: in phase 1 a feasible solution is obtained that is used as an initial starting point in phase 2. In the latter, a biconvex problem equivalent to the original problem is solved … Read more

    On the Numerical Performance of Derivative-Free Optimization Methods Based on Finite-Difference Approximations

  • Jorge Nocedal
  • Hao-Jun Shi
  • Melody Xuan
  • Figen Oztoprak
    • Categories Nonlinear Optimization Tags , , , ,

    The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing gradients of a smoothed approximation of the objective function (and constraints), and employing them within established codes. These … Read more

    Decomposition Methods for Global Solutions of Mixed-Integer Linear Programs

  • Kaizhao Sun
  • Wotao Yin
  • Mou Sun
    • Categories (Mixed) Integer Linear Programming, Global Optimization Tags , ,

    This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which aim to take advantage of separable structures of the original problem by solving a sequence of lower-dimensional MILPs. The first method is based on the $\ell_1$-augmented Lagrangian method (ALM), and the second one is based on a modified alternating direction method of … Read more

    An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems

  • Tianxiang Liu
  • Akiko Takeda
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this paper, we propose a new method for a class of difference-of-convex (DC) optimization problems, whose objective is the sum of a smooth function and a possibly non-prox-friendly DC function. The method sequentially solves subproblems constructed from a quadratic approximation of the smooth function and a linear majorization of the concave part of the … Read more

    Direct-Search for a Class of Stochastic Min-Max Problems

  • Sotiris Anagnostidis
  • Youssef Diouane
  • Aurelien Lucchi
    • Categories Nonlinear Optimization

    Recent applications in machine learning have renewed the interest of the community in min-max optimization problems. While gradient-based optimization methods are widely used to solve such problems, there are however many scenarios where these techniques are not well-suited, or even not applicable when the gradient is not accessible. We investigate the use of direct-search methods … Read more

    Optimal Hospital Care Scheduling During the SARS-CoV-2 Pandemic

  • Josh D'Aeth
  • Shubhechyya Ghosal
  • Fiona Grimm
  • David Haw
  • Esma Koca
  • Krystal Lau
  • Huikang Liu
  • Stefano Moret
  • Dheeya Rizmie
  • Peter Smith
  • Giovanni Forchini
  • Marisa Miraldo
  • Wolfram Wiesemann
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags , , ,

    The COVID-19 pandemic has seen dramatic demand surges for hospital care that have placed a severe strain on health systems worldwide. As a result, policy makers are faced with the challenge of managing scarce hospital capacity so as to reduce the backlog of non-COVID patients whilst maintaining the ability to respond to any potential future … Read more

    Robust Optimization in Nanoparticle Technology: A Proof of Principle by Quantum Dot Growth in a Residence Time Reactor

  • Kevin-Martin Aigner
  • Frauke Liers
  • Jana Dienstbier
  • Wolfgang Peukert
  • Lukas Pflug
  • Jan Hendrik Rolfes
  • Doris Segets
    • Categories Chemical Engineering, Robust Optimization Tags , , ,

    Knowledge-based determination of the best-possible experimental setups for nanoparticle design is highly challenging. Additionally, such processes are accompanied by noticeable uncertainties. Therefore, protection against these uncertainties is needed. Robust optimization helps determining such best possible processes. The latter guarantees quality requirements regardless of how the uncertainties, e.g. with regard to variations in raw materials, heat … Read more