A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization

  • Nicolas Gillis
  • Le Thi Khanh Hien
  • Duy Nhat Phan
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this paper, we propose an algorithmic framework dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our framework employs the general minimization-majorization (MM) principle to update each block of variables so as to not only unify the convergence analysis of previous … Read more

    Controllable Transmission Networks UnderDemand Uncertainty with Modular FACTS

  • Alireza Soroudi
    • Categories Constrained Nonlinear Optimization, Optimization Software and Modeling Systems, Scheduling Tags , ,

    The transmission system operators (TSOs) are responsible to provide secure and efficient access to the transmission system for all stakeholders. This task is gradually getting challenging due to the demand growth, demand uncertainty, rapid changes in generation mix, and market policies. Traditionally, the TSOs try to maximize the technical performance of the transmission network via … Read more

    An Approximation Algorithm for Indefinite Mixed Integer Quadratic Programming

  • Alberto Del Pia
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory

    In this paper we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer variables are fixed. The running time of the algorithm is expected unless P=NP. In order to design … Read more

    Sparse Approximations with Interior Point Methods

  • Valentina De Simone
  • Daniela di Serafino
  • Jacek Gondzio
  • Spyridon Pougkakiotis
  • Marco Viola
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , , , ,

    Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience … Read more

    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

    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

    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

    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

    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