Nonlinear Optimization

String-Averaging Methods for Best Approximation to Common Fixed Point Sets of Operators: The Finite and Infinite Cases

  • Yair Censor
  • Ariel Nisenbaum
    • Categories Convex Optimization, Nonlinear Optimization, Parallel Algorithms

    Abstract String-averaging is an algorithmic structure used when handling a family of operators in situations where the algorithm at hand requires to employ the operators in a specific order. Sequential orderings are well-known and a simultaneous order means that all operators are used simultaneously (in parallel). String-averaging allows to use strings of indices, constructed by … Read more

    Active-set identification with complexity guarantees of an almost cyclic 2-coordinate descent method with Armijo line search

  • Andrea Cristofari
    • Categories Constrained Nonlinear Optimization

    In this paper, it is established finite active-set identification of an almost cyclic 2-coordinate descent method for problems with one linear coupling constraint and simple bounds. First, general active-set identification results are stated for non-convex objective functions. Then, under convexity and a quadratic growth condition (satisfied by any strongly convex function), complexity results on the … Read more

    A Penalty-free Infeasible Approach for a Class of Nonsmooth Optimization Problems over the Stiefel Manifold

  • Nachuan Xiao
  • Xin Liu
  • Ya-xiang Yuan
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. For smooth and L21-norm regularized cases, these infeasible approaches adopt simple and orthonormalization-free updating schemes and show high efficiency in some numerical experiments. However, to avoid orthonormalization while enforcing the feasibility of the final … 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

    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

    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

    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

    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

    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