Year: 2017

Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems

  • Jiang Hao
  • Cheng Lizhi
  • Sun Tao
    • Categories Nonlinear Optimization

    In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both mathematics and computations in solving the nonconvex and nonsmooth subproblem. In view of this, we propose a reweighted alternating direction method of … Read more

    Inner Conditions for Error Bounds and Metric Subregulerity of Multifunctions

  • Dominique Azé
    • Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Nonlinear Optimization Tags , , , , ,

    We introduce a new class of sets, functions and multifunctions which is shown to be large and to enjoy some nice common properties with the convex setting. Error bounds for objects attached to this class are characterized in terms of inner conditions of Abadie’s type, that is conditions bearing on normal cones and coderivatives at … Read more

    A convergence frame for inexact nonconvex and nonsmooth algorithms and its applications to several iterations

  • Jiang Hao
  • Cheng Lizhi
  • Sun Tao
  • Zhu Wei
    • Categories Nonlinear Optimization

    In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which both are related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a wide of classical inexact nonconvex … Read more

    Worst-case convergence analysis of gradient and Newton methods through semidefinite programming performance estimation

  • Etienne de Klerk
  • François Glineur
  • Adrien B. Taylor
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    We provide new tools for worst-case performance analysis of the gradient (or steepest descent) method of Cauchy for smooth strongly convex functions, and Newton’s method for self-concordant functions. The analysis uses semidefinite programming performance estimation, as pioneered by Drori en Teboulle [Mathematical Programming, 145(1-2):451–482, 2014], and extends recent performance estimation results for the method of … Read more

    An incremental mirror descent subgradient algorithm with random sweeping and proximal step

  • Axel Böhm
  • Radu Ioan Bot
    • Categories Convex Optimization, Stochastic Programming

    We investigate the convergence properties of incremental mirror descent type subgradient algorithms for minimizing the sum of convex functions. In each step we only evaluate the subgradient of a single component function and mirror it back to the feasible domain, which makes iterations very cheap to compute. The analysis is made for a randomized selection … Read more

    Same-Day Delivery with Drone Resupply

  • John-Paul Clarke
  • Iman Dayarian
  • Martin Savelsbergh
    • Categories Applications - OR and Management Sciences, Transportation

    Unmanned Aerial Vehicles (UAVs), commonly referred to as drones, have recently seen an increased level of interest as their potential use in same-day home delivery has been promoted and advocated by large retailers and courier delivery companies. We introduce a novel way to exploit drones in same-day home delivery settings: drone resupply. We consider a … Read more

    Convergence Analysis of Processes with Valiant Projection Operators in Hilbert Space

  • Yair Censor
  • Rafiq Mansour
    • Categories Constrained Nonlinear Optimization, Convex Optimization

    Convex feasibility problems require to find a point in the intersection of a finite family of convex sets. We propose to solve such problems by performing set-enlargements and applying a new kind of projection operators called valiant projectors. A valiant projector onto a convex set implements a special relaxation strategy, proposed by Goffin in 1971, … Read more

    Perturbation analysis of a class of conic programming problems under Jacobian uniqueness conditions

  • Ziran Yin
  • Liwei Zhang
    • Categories Linear, Cone and Semidefinite Programming, Second-Order Cone Programming, Semi-definite Programming

    We consider the stability of a class of parameterized conic programming problems which are more general than the C2-smooth parameterization. We show that when the Karush-Kuhn-Tucker (KKT) condition, the constraint nondegeneracy condition, the strict complementary condition and the second order sucient condition (named as Jacobian uniqueness conditions here) are satis ed at a feasible point of … Read more

    Modeling Time-dependent Randomness in Stochastic Dual Dynamic Programming

  • Nils Löhndorf
  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , ,

    We consider the multistage stochastic programming problem where uncertainty enters the right-hand sides of the problem. Stochastic Dual Dynamic Programming (SDDP) is a popular method to solve such problems under the assumption that the random data process is stagewise independent. There exist two approaches to incorporate dependence into SDDP. One approach is to model the … Read more

    Complementarity-Based Nonlinear Programming Techniques for Optimal Mixing in Gas Networks

  • Falk M. Hante
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Complementarity and Variational Inequalities, Nonlinear Optimization Tags , , , ,

    We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we … Read more