large-scale optimization

Adaptive Augmented Lagrangian Methods: Algorithms and Practical Numerical Experience

  • Frank E. Curtis
  • Nicholas I. M. Gould
  • Daniel P. Robinson
  • Hao Jiang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed adaptive AL trust region method by Curtis et al. [An adaptive augmented Lagrangian method for large-scale constrained optimization, Math. Program. 152 (2015), pp.201–245.]. … Read more

    Fast Projection onto the Simplex and the l1 Ball

  • Laurent Condat
    • Categories Applications - OR and Management Sciences, Convex and Nonsmooth Optimization Tags , ,

    A new algorithm is proposed to project, exactly and in finite time, a vector of arbitrary size onto a simplex or a l1-norm ball. The algorithm is demonstrated to be faster than existing methods. In addition, a wrong statement in a paper by Duchi et al. is corrected and an adversary sequence for Michelot’s algorithm … Read more

    Robust Block Coordinate Descent

  • Kimon Fountoulakis
  • Rachael Tappenden
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Robust Coordinate Descent (RCD). At … Read more

    Projection methods in quantum information science

  • Yuen-Lam Cheung
  • Dmitriy Drusvyatskiy
  • Henry Wolkowicz
  • Chi-Kwong Li
  • Diane Pelejo
    • Categories Linear, Cone and Semidefinite Programming, Other Topics Tags , , , , , ,

    We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\{\rho_1, \dots, \rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other words, we must find a {\em completely positive linear map}, if it exists, that maps a given set of density matrices to … Read more

    OSGA: A fast subgradient algorithm with optimal complexity

  • Arnold Neumaier
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , , , ,

    This paper presents an algorithm for approximately minimizing a convex function in simple, not necessarily bounded convex domains, assuming only that function values and subgradients are available. No global information about the objective function is needed apart from a strong convexity parameter (which can be put to zero if only convexity is known). The worst … Read more

    Distributed Optimization Methods for Large Scale Optimal Control

  • Attila Kozma
    • Categories Optimization of Simulated Systems, Quadratic Programming Tags , , , , ,

    This thesis aims to develop and implement both nonlinear and linear distributed optimization methods that are applicable, but not restricted to the optimal control of distributed systems. Such systems are typically large scale, thus the well-established centralized solution strategies may be computationally overly expensive or impossible and the application of alternative control algorithms becomes necessary. … Read more

    Eigenvalue, Quadratic Programming, and Semidefinite Programming Relaxations for a Cut Minimization Problem

  • Ting Kei Pong
  • Henry Wolkowicz
  • Hao Sun
  • Ningchuan Wang
    • Categories Combinatorial Optimization, Graphs and Matroids, Semi-definite Programming Tags , , , ,

    We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex separator. This problem is closely related to the graph partitioning problem. In … Read more

    An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization

  • Frank E. Curtis
  • Nicholas I. M. Gould
  • Daniel P. Robinson
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, … Read more

    A First Course in Linear Optimization, version 3.0

  • Jon Lee
    • Categories (Mixed) Integer Linear Programming, Linear Programming, Other Topics Tags , ,

    This is the “front matter” of a new open-source book on Linear Optimization. The book and associated Matlab/AMPL/Mathematica programs are freely available from: https://sites.google.com/site/jonleewebpage/home/publications/#book CitationJon Lee, “A First Course in Linear Optimization”, Third Edition, Reex Press, 2013-2017.ArticleDownload View PDF

    An inexact block-decomposition method for extra large-scale conic semidefinite programming

  • Renato D.C. Monteiro
  • Camilo Ortiz
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , , , , , ,

    In this paper, we present an inexact block-decomposition (BD) first-order method for solving standard form conic semidefinite programming (SDP) which avoids computations of exact projections onto the manifold defined by the affine constraints and, as a result, is able to handle extra large SDP instances. The method is based on a two-block reformulation of the … Read more