nonsmooth optimization

On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems

  • Welington de Oliveira
  • Yongjia Song
  • Wim van Ackooij
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , ,

    We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing iterates during the solution process. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. Numerical experiments on a hydrothermal scheduling … Read more

    An Algorithm for Nonsmooth Optimization by Successive Piecewise Linearization

  • Sabrina Fiege
  • Andreas Griewank
  • Andrea Walther
    • Categories Nonsmooth Optimization Tags , , , ,

    We present an optimization method for Lipschitz continuous, piecewise smooth (PS) objective functions based on successive piecewise linearization. Since, in many realistic cases, nondifferentiabilities are caused by the occurrence of abs(), max(), and min(), we concentrate on these nonsmooth elemental functions. The method’s idea is to locate an optimum of a PS objective function by … Read more

    A Primal-Dual Homotopy Algorithm for l_1-Minimization with l_inf-Constraints

  • Christoph Brauer
  • Dirk A. Lorenz
  • Andreas M. Tillmann
    • Categories Convex Optimization, Linear Programming Tags , , , ,

    In this paper we propose a primal-dual homotopy method for $\ell_1$-minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints and we show that there exists a piecewise linear solution path with finitely many break points for the primal problem … Read more

    Accelerated first-order methods for large-scale convex minimization

  • Masoud Ahookhosh
    • Categories Applications - OR and Management Sciences, Convex and Nonsmooth Optimization, Convex Optimization Tags , , , , ,

    This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\”older continuous gradients. The proposed schemes are optimal for smooth strongly convex problems with Lipschitz continuous gradients and optimal up to a logarithmic factor for nonsmooth problems … Read more

    Lagrangian relaxation for SVM feature selection

  • Manlio Gaudioso
  • Enrico Gorgone
  • Martine Labbé
  • Antonio M. Rodríguez-Chía
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in a standard L1 norm Support Vector Machine (SVM) framework for binary classification. The feature selection model we adopt is a Mixed Binary Linear Programming problem and it is suitable for a Lagrangian relaxation approach. Based on a property of the optimal multiplier setting, we … Read more

    New Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure

  • Robert M. Freund
  • Haihao Lu
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , ,

    Motivated by recent work of Renegar, we present new computational methods and associated computational guarantees for solving convex optimization problems using first-order methods. Our problem of interest is the general convex optimization problem f^* = \min_{x \in Q} f(x), where we presume knowledge of a strict lower bound f_slb < f^*. [Indeed, f_slb is naturally ... Read more

    A forward-backward dynamical approach to the minimization of the sum of a nonsmooth convex with a smooth nonconvex function

  • Radu Ioan Bot
  • Ernö Robert Csetnek
    • Categories Nonsmooth Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We address the minimization of the sum of a proper, convex and lower semicontinuous with a (possibly nonconvex) smooth function from the perspective of an implicit dynamical system of forward-backward type. The latter is formulated by means of the gradient of the smooth function and of the proximal point operator of the nonsmooth one. The … Read more

    On the convergence rate of an inexact proximal point algorithm for quasiconvex minimization on Hadamard manifolds

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Global Optimization Tags , , , , ,

    In this paper we present a rate of convergence analysis of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem. Article Download View On the … Read more

    An O(1/k) Convergence Rate for the Variable Stepsize Bregman Operator Splitting Algorithm

  • William W. Hager
  • Maryam Yashtini
  • Hongchao Zhang
    • Categories Nonsmooth Optimization Tags , , , , ,

    An earlier paper proved the convergence of a variable stepsize Bregman operator splitting algorithm (BOSVS) for minimizing $\phi(Bu)+H(u)$ where $H$ and $\phi$ are convex functions, and $\phi$ is possibly nonsmooth. The algorithm was shown to be relatively efficient when applied to partially parallel magnetic resonance image reconstruction problems. In this paper, the convergence rate of … Read more