convergence analysis

On the Convergence Results of a class of Nonmonotone Accelerated Proximal Gradient Methods for Nonsmooth and Nonconvex Minimization Problems

  • Hongwei Liu
  • Wang Ting
    • Categories Nonsmooth Optimization Tags , ,

    In this paper, we consider a class of nonsmooth problem that is the sum of a Lipschitz differentiable function and a nonsmooth and proper lower semicontinuous function. We discuss here the convergence rate of the function values for a nonmonotone accelerated proximal gradient method, which proposed in “Huan Li and Zhouchen Lin: Accelerated proximal gradient … Read more

    A Nonmonontone Accelerated Proximal Gradient Method with Variable Stepsize Strategy for Nonsmooth and Nonconvex Minimization Problems

  • Hongwei Liu
  • Wang Ting
    • Categories Nonsmooth Optimization Tags , , , , ,

    We propose a new nonmonontone accelerated proximal gradient method with variable stepsize strategy for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. In this algorithm, the objective function value be allowed to increase discontinuously, but is decreasing from the overall point of view. The variable stepsize strategy don’t … Read more

    Price Optimization with Practical Constraints

  • Lanshan Han
  • Hsin-Chan Huang
  • Alvin Lim
  • Xiaojie Wang
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Yield Management Tags , , , , ,

    In this paper, we study a retailer price optimization problem which includes the practical constraints: maximum number of price changes and minimum amount of price change (if a change is recommended). We provide a closed-form formula for the Euclidean projection onto the feasible set defined by these two constraints, based on which a simple gradient … Read more

    Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems

  • Richard Krug
  • Günter Leugering
  • Martin Schmidt
  • Dieter Weninger
  • Alexander Martin
    • Categories Systems governed by Differential Equations Optimization Tags , , , ,

    In this article, we extend the time-domain decomposition method described by Lagnese and Leugering (2003) to semilinear optimal control problems for hyperbolic balance laws with spatio-temporal varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis … Read more

    Convergence of Proximal Gradient Algorithm in the Presence of Adjoint Mismatch

  • Émilie Chouzenoux
  • Jean-Christophe Pesquet
  • Cyril Riddel
  • Marion Savanier
  • Yves Trousset
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , ,

    We consider the proximal gradient algorithm for solving penalized least-squares minimization problems arising in data science. This first-order algorithm is attractive due to its flexibility and minimal memory requirements allowing to tackle large-scale minimization problems involving non-smooth penalties. However, for problems such as X-ray computed tomography, the applicability of the algorithm is dominated by the … Read more

    Online matrix factorization for Markovian data and applications to Network Dictionary Learning

  • Laura Balzano
  • Hanbaek Lyu
  • Deanna Needell
    • Categories Data-Mining, Nonlinear Optimization Tags , , , ,

    Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of complex data sets in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of a dependent data stream remains largely … Read more

    Convergence Analysis and a DC Approximation Method for Data-driven Mathematical Programs with Distributionally Robust Chance Constraints

  • Hailin Sun
  • Chen Yannan
  • Dali Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    In this paper, we consider the convergence analysis of data-driven mathematical programs with distributionally robust chance constraints (MPDRCC) under weaker conditions without continuity assumption of distributionally robust probability functions. Moreover, combining with the data-driven approximation, we propose a DC approximation method to MPDRCC without some special tractable structures. We also give the convergence analysis of … Read more

    Penalized stochastic gradient methods for stochastic convex optimization with expectation constraints

  • Xiantao Xiao
    • Categories Stochastic Programming Tags , , , ,

    Stochastic gradient method and its variants are simple yet effective for minimizing an expectation function over a closed convex set. However, none of these methods are applicable to solve stochastic programs with expectation constraints, since the projection onto the feasible set is prohibitive. To deal with the expectation constrained stochastic convex optimization problems, we propose … Read more

    Stabilized Barzilai-Borwein method

  • Oleg Burdakov
  • Yu-Hong Dai
  • Na Huang
    • Categories Unconstrained Optimization Tags , , ,

    The Barzilai-Borwein (BB) method is a popular and efficient tool for solving large-scale unconstrained optimization problems. Its search direction is the same as for the steepest descent (Cauchy) method, but its stepsize rule is different. Owing to this, it converges much faster than the Cauchy method. A feature of the BB method is that it … Read more

    General Convergence Rates Follow From Specialized Rates Assuming Growth Bounds

  • Benjamin Grimmer
    • Categories Convex Optimization Tags , ,

    Often in the analysis of first-order methods, assuming the existence of a quadratic growth bound (a generalization of strong convexity) facilitates much stronger convergence analysis. Hence the analysis is done twice, once for the general case and once for the growth bounded case. We give a meta-theorem for deriving general convergence rates from those assuming … Read more