Nonlinear Optimization

Complexity of a Projected Newton-CG Method for Optimization with Bounds

  • Yue Xie
  • Stephen Wright
    • Categories Bound-constrained Optimization Tags , , , ,

    This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained optimization and a recently proposed Newton-conjugate gradient algorithm for unconstrained nonconvex optimization. Using a new definition of approximate … Read more

    Fast cluster detection in networks by first-order optimization

  • Immanuel M. Bomze
  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Network Optimization, Nonlinear Optimization Tags , , ,

    Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we … Read more

    An inexact restoration-nonsmooth algorithm with variable accuracy for stochastic nonsmooth convex optimization problems in machine learning and stochastic linear complementarity problems

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Tijana Ostojić
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using Inexact Restoration-based adapted sample sizes. The sample size is chosen in an adaptive manner based on Inexact Restoration. The algorithm uses line search … Read more

    Universal Conditional Gradient Sliding for Convex Optimization

  • Yuyuan Ouyang
  • Trevor Squires
    • Categories Convex Optimization, Nonlinear Optimization Tags , , , ,

    In this paper, we present a first-order projection-free method, namely, the universal conditional gradient sliding (UCGS) method, for solving ε-approximate solutions to convex differentiable optimization problems. For objective functions with Hölder continuous gradients, we show that UCGS is able to terminate with ε-solutions with at most O((1/ε)^(2/(1+3v))) gradient evaluations and O((1/ε)^(4/(1+3v))) linear objective optimizations, where … Read more

    Further developments of methods for traversing regions of non-convexity in optimization problems

  • Michael Bartholomew-Biggs
  • Salah Beddiaf
  • Bruce Christianson
    • Categories Unconstrained Optimization Tags , ,

    This paper continues to address one of its author’s obsession with the well- known problem of dealing with non-convexity during the minimization of a nonlinear function f(x) by Newton-like methods. It builds on some proposals made by the present authors in “A Comparison of methods for traversing regions of non-convexity in optimization problems”. (Numerical Algorithms … Read more

    Robust Price Optimization of Multiple Products under Interval Uncertainties

  • Mahdi Hamzeei
  • Alvin Lim
  • Jiefeng Xu
    • Categories Constrained Nonlinear Optimization, Robust Optimization, Yield Management Tags , ,

    In this paper, we solve the multiple product price optimization problem under interval uncertainties of the price sensitivity parameters in the demand function. The objective of the price optimization problem is to maximize the overall revenue of the firm where the decision variables are the prices of the products supplied by the firm. We propose … Read more

    Use of static surrogates in hyperparameter optimization

  • Dounia Lakhmiri
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems Tags , ,

    Optimizing the hyperparameters and architecture of a neural network is a long yet necessary phase in the development of any new application. This consuming process can benefit from the elaboration of strategies designed to quickly discard low quality configurations and focus on more promising candidates. This work aims at enhancing HyperNOMAD, a library that adapts … Read more

    Global convergence of Riemannian line search methods with a Zhang-Hager-type condition

  • Harry Oviedo
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper, we analyze the global convergence of a general non–monotone line search method on Riemannian manifolds. For this end, we introduce some properties for the tangent search directions that guarantee the convergence, to a stationary point, of this family of optimization methods under appropriate assumptions. A modified version of the non–monotone line search … Read more

    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