Nonsmooth Optimization

Dini Derivative and a Characterization for Lipschitz and Convex Functions on Riemannian Manifolds

  • Orizon Pereira Ferreira
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , ,

    Dini derivative on Riemannian manifold setting is studied in this paper. In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality conditions for constraint optimization problems in terms of the Dini derivative are given. Article Download View Dini Derivative and a Characterization for Lipschitz and Convex Functions on Riemannian … Read more

    Large Scale Portfolio Optimization with Piecewise Linear Transaction Costs

  • Potaptchik Marina
  • Levent Tunçel
  • Henry Wolkowicz
    • Categories Finance and Economics, Nonsmooth Optimization, Quadratic Programming Tags , , ,

    We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model of the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle … Read more

    Discrete gradient method: a derivative free method for nonsmooth optimization

  • Adil Bagirov
  • Bulent Karasozen
  • Meral Sezer
    • Categories Nonsmooth Optimization Tags , , ,

    In this paper a new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can … Read more

    Benchmark of Some Nonsmooth Optimization Solvers for Computing Nonconvex Proximal Points

  • Warren Hare
  • Claudia Sagastizábal
    • Categories Nonsmooth Optimization, Optimization Software Benchmark Tags , ,

    The major focus of this work is to compare several methods for computing the proximal point of a nonconvex function via numerical testing. To do this, we introduce two techniques for randomly generating challenging nonconvex test functions, as well as two very specific test functions which should be of future interest to Nonconvex Optimization Benchmarking. … Read more

    Smooth minimization of two-stage stochastic linear programs

  • Shabbir Ahmed
    • Categories Nonsmooth Optimization, Stochastic Programming Tags ,

    This note presents an application of the smooth optimization technique of Nesterov for solving two-stage stochastic linear programs. It is shown that the original O(1/e) bound of Nesterov on the number of main iterations required to obtain an e-optimal solution is retained. Citation Technical Report, School of Industrial & Systems Engineering, Georgia Institute of Technology, … Read more

    Stationarity and Regularity of Real-Valued Functions

  • Alexander Y. Kruger
    • Categories Nonsmooth Optimization Tags , , , , , , , ,

    Different stationarity and regularity concepts for extended real-valued functions on metric spaces are considered in the paper. The properties are characterized in terms of certain local constants. A classification scheme for stationarity/regularity constants and corresponding concepts is proposed. The relations between different constants are established. Citation University of Ballarat, School of Information Technology and Mathematical … Read more

    A conic interior point decomposition approach for large scale semidefinite programming

  • Gema Plaza
  • Kartik Krishnan Sivaramakrishnan
  • Tamás Terlaky
    • Categories Nonsmooth Optimization, Semi-definite Programming Tags , , ,

    We describe a conic interior point decomposition approach for solving a large scale semidefinite programs (SDP) whose primal feasible set is bounded. The idea is to solve such an SDP using existing primal-dual interior point methods, in an iterative fashion between a {\em master problem} and a {\em subproblem}. In our case, the master problem … Read more

    Primal interior-point method for large sparse minimax optimization.

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags ,

    In this paper, we propose an interior-point method for large sparse minimax optimization. After a short introduction, where various barrier terms are discussed, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus nonconvex problems can be solved successfully. The results … Read more

    Trust-region interior-point method for large sparse l_1 optimization.

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags ,

    In this paper, we propose an interior-point method for large sparse l_1 optimization. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus nonconvex problems can be solved successfully. The results of computational experiments given in this … Read more

    Fast Moreau Envelope Computation I: Numerical Algorithms

  • Yves Lucet
    • Categories Convex Optimization, Nonsmooth Optimization, Problem Solving Environments Tags , , , , , ,

    The present article summarizes the state of the art algorithms to compute the discrete Moreau envelope, and presents a new linear-time algorithm, named NEP for NonExpansive Proximal mapping. Numerical comparisons between the NEP and two existing algorithms: The Linear-time Legendre Transform (LLT) and the Parabolic Envelope (PE) algorithms are performed. Worst-case time complexity, convergence results, … Read more