Nonlinear Optimization

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

    A Penalty-free Infeasible Approach for a Class of Nonsmooth Optimization Problems over the Stiefel Manifold

  • Nachuan Xiao
  • Xin Liu
  • Ya-xiang Yuan
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. For smooth and L21-norm regularized cases, these infeasible approaches adopt simple and orthonormalization-free updating schemes and show high efficiency in some numerical experiments. However, to avoid orthonormalization while enforcing the feasibility of the final … Read more

    Controllable Transmission Networks UnderDemand Uncertainty with Modular FACTS

  • Alireza Soroudi
    • Categories Constrained Nonlinear Optimization, Optimization Software and Modeling Systems, Scheduling Tags , ,

    The transmission system operators (TSOs) are responsible to provide secure and efficient access to the transmission system for all stakeholders. This task is gradually getting challenging due to the demand growth, demand uncertainty, rapid changes in generation mix, and market policies. Traditionally, the TSOs try to maximize the technical performance of the transmission network via … Read more

    A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization

  • Nicolas Gillis
  • Le Thi Khanh Hien
  • Duy Nhat Phan
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this paper, we propose an algorithmic framework dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our framework employs the general minimization-majorization (MM) principle to update each block of variables so as to not only unify the convergence analysis of previous … Read more