dc programming

Minimizing the difference of convex and weakly convex functions via bundle method

  • Ksenia Syrtseva
  • Welington de Oliveira
  • Sophie Demassey
  • Wim van Ackooij
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    We consider optimization problems with objective and constraint being the difference of convex and weakly convex functions. This framework covers a vast family of nonsmooth and nonconvex optimization problems, particularly those involving Difference-of-Convex (DC) functions with known DC decomposition, functions whose gradient is Lipschitz continuous, as well as problems that comprise certain classes of composite … Read more

    An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems

  • Tianxiang Liu
  • Akiko Takeda
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this paper, we propose a new method for a class of difference-of-convex (DC) optimization problems, whose objective is the sum of a smooth function and a possibly non-prox-friendly DC function. The method sequentially solves subproblems constructed from a quadratic approximation of the smooth function and a linear majorization of the concave part of the … Read more

    Clustering and Multifacility Location with Constraints via Distance Function Penalty Method and DC Programming

  • Nguyen Thai An
  • Nguyen Mau Nam
  • Sam Reynolds
  • Tuyen Tran
    • Categories Nonsmooth Optimization Tags , , ,

    This paper is a continuation of our effort in using mathematical optimization involving DC programming in clustering and multifacility location. We study a penalty method based on distance functions and apply it particularly to a number of problems in clustering and multifacility location in which the centers to be found must lie in some given … Read more

    A TVSCAD approach for image deblurring with impulsive noise

  • Guoyong Gu
  • Junfeng Yang
  • Suhong Jiang
    • Categories Nonsmooth Optimization Tags , , , , , , , ,

    We consider image deblurring problem in the presence of impulsive noise. It is known that \emph{total variation} (TV) regularization with L1-norm penalized data fitting (TVL1 for short) works reasonably well only when the level of impulsive noise is relatively low. For high level impulsive noise, TVL1 works poorly. The reason is that all data, both … Read more

    On globally solving the maximum weighted clique problem

  • Nam Nguyen Canh
    • Categories Applications - OR and Management Sciences Tags , , , ,

    In this paper, we consider a combinatorial optimization problem, the Maximum Weighted Clique Problem (MWCP), a NP-hard problem. The considered problem is first formulated in the form of binary constrained quadratic program and then reformulated as a Difference Convex (DC) program. A global optimal solution is found by applying DC Algorithm (DCA) in combining with … Read more

    Conic separation of finite sets: The non-homogeneous case

  • Annabella Astorino
  • Manlio Gaudioso
  • Alberto Seeger
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , ,

    We address the issue of separating two finite sets in $\mathbb{R}^n $ by means of a suitable revolution cone $$ \Gamma (z,y,s)= \{x \in \mathbb{R}^n :\, s\,\Vert x-z\Vert – y^T(x-z)=0\}.$$ One has to select the aperture coefficient $s$, the axis $y$, and the apex $z$ in such a way as to meet certain optimal separation … Read more

    Locating a competitive facility in the plane with a robustness criterion

  • Rafael Blanquero
  • Emilio Carrizosa
  • Eligius M.T. Hendrix
    • Categories Facility Planning and Design, Global Optimization Applications, Robust Optimization Tags , , , , , ,

    A new continuous location model is presented and embedded in the literature on robustness in facility location. The multimodality of the model is investigated, and a branch and bound method based on dc optimization is described. Numerical experience is reported, showing that the developed method allows one to solve in a few seconds problems with … Read more