Equivalence and Strong Equivalence between Sparsest and Least l1-Norm Nonnegative Solutions of Linear Systems and Their Application

  • Yun-Bin Zhao
    • Categories Convex Optimization, Global Optimization, Linear Programming Tags , , , ,

    Many practical problems can be formulated as $\ell_0$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative solutions to underdetermined linear systems. Recent study indicates that $\ell_1$-minimization is efficient for solving some classes of $\ell_0$-minimization problems. From a mathematical point of view, however, the understanding of the relationship between $\ell_0$- and $\ell_1$-minimization remains incomplete. In … Read more

    Worst-Case Performance Analysis of Some Approximation Algorithms for Minimizing Makespan and Flow-Time

  • Michael Huang
  • Peruvemba Sundaram Ravi
  • Levent Tunçel
    • Categories Approximation Algorithms, Scheduling Tags , , ,

    In 1976, Coffman and Sethi conjectured that a natural extension of LPT list scheduling to the bicriteria scheduling problem of minimizing makespan over flowtime optimal schedules, called LD algorithm, has a simple worst-case performance bound: (5m-2)/(4m-1) , where m is the number of machines. We study structure of potential minimal counterexamples to this conjecture and … Read more

    Preconditioning issues in the numerical solution of nonlinear equations and nonlinear least squares

  • Stefania Bellavia
  • Margherita Porcelli
    • Categories Nonlinear Optimization Tags , ,

    Second order methods for optimization call for the solution of sequences of linear systems. In this survey we will discuss several issues related to the preconditioning of such sequences. Covered topics include both techniques for building updates of factorized preconditioners and quasi-Newton approaches. Sequences of unsymmetric linear systems arising in Newton- Krylov methods will be … Read more

    An Improvised Approach to Robustness in Linear Optimization

  • Mehdi Karimi
  • Somayeh Moazeni
  • Levent Tunçel
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags ,

    We treat uncertain linear programming problems by utilizing the notion of weighted analytic centers and notions from the area of multi-criteria decision making. In addition to many practical advantages, due to the flexibility of our approach, we are able to prove that the robust optimal solutions generated by our algorithms are at least as desirable … Read more

    Multiple-choice Vector Bin Packing: Arc-flow Formulation with Graph Compression

  • Filipe Brandão
  • João Pedro Pedroso
    • Categories (Mixed) Integer Linear Programming Tags , ,

    The vector bin packing problem (VBP) is a generalization of bin packing with multiple constraints. In this problem we are required to pack items, represented by p-dimensional vectors, into as few bins as possible. The multiple-choice vector bin packing (MVBP) is a variant of the VBP in which bins have several types and items have … 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

    The inexact projected gradient method for quasiconvex vector optimization problems

  • Yunier Bello-Cruz
  • Glaydston Bento
  • Gemayqzel Bouza
  • R.F.B. Costa
    • Categories Generalized Convexity/Monoticity, Multi-Criteria Optimization, Nonlinear Optimization

    Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is important to have practical solution approaches for computing. In this work, we consider the inexact projected gradient-like method for … Read more

    A Relaxed-Projection Splitting Algorithm for Variational Inequalities in Hilbert Spaces

  • Yunier Bello-Cruz
  • R. Diaz Millan
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous convex function inequality. In our scheme, the orthogonal projections onto the feasible set are replaced by projections onto separating hyperplanes. Furthermore, each … Read more

    Lagrangean Decomposition for Mean-Variance Combinatorial Optimization

  • Frank Baumann
  • Christoph Buchheim
  • Anna Ilyina
    • Categories Combinatorial Optimization, Constrained Nonlinear Optimization, Robust Optimization Tags , ,

    We address robust versions of combinatorial optimization problems, focusing on the uncorrelated ellipsoidal uncertainty case, which corresponds to so-called mean-variance optimization. We present a branch and bound-algorithm for such problems that uses lower bounds obtained from Lagrangean decomposition. This approach allows to separate the uncertainty aspect in the objective function from the combinatorial structure of … Read more