Welington de Oliveira

A progressive decoupling algorithm for minimizing the difference of convex and weakly convex functions over a linear subspace

  • Welington de Oliveira
  • João Carlos Souza
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    Commonly, decomposition and splitting techniques for optimization problems strongly depend on convexity. Implementable splitting methods for nonconvex and nonsmooth optimization problems are scarce and often lack convergence guarantees. Among the few exceptions is the Progressive Decoupling Algorithm (PDA), which has local convergence should convexity be elicitable. In this work, we furnish PDA with a descent … Read more

    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 certain classes of composite and nonconvex value functions. We investigate several stationary conditions and extend the proximal bundle algorithm of [van Ackooij et … Read more

    Revisiting Augmented Lagrangian Duals

  • Marcelo Cordova
  • Welington de Oliveira
  • Claudia Sagastizábal
    • Categories Nonsmooth Optimization Tags , ,

    For nonconvex optimization problems, possibly having mixed-integer variables, a convergent primal-dual solution algorithm is proposed. The approach applies a proximal bundle method to certain augmented Lagrangian dual that arises in the context of the so-called generalized augmented Lagrangians. We recast these Lagrangians into the framework of a classical Lagrangian, by means of a special reformulation … Read more

    A bundle method for nonsmooth DC programming with application to chance-constrained problems

  • Welington de Oliveira
  • Sophie Demassey
  • Paul Javal
  • Hugo Morais
  • Bhargav Swaminathan
  • Wim van Ackooij
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags

    This work considers nonsmooth and nonconvex optimization problems whose objective and constraint functions are defined by difference-of-convex (DC) functions. We consider an infeasible bundle method based on the so-called improvement functions to compute critical points for problems of this class. Our algorithm neither employs penalization techniques nor solves subproblems with linearized constraints. The approach, which … Read more

    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 Adaptive Partition-based Level Decomposition for Solving Two-stage Stochastic Programs with Fixed Recourse

  • Welington de Oliveira
  • Yongjia Song
  • Wim van Ackooij
    • Categories Stochastic Programming

    We present a computational study of several strategies to solve two-stage stochastic linear programs by integrating the adaptive partition-based approach with level decomposition. A partition-based formulation is a relaxation of the original stochastic program, obtained by aggregating variables and constraints according to a scenario partition. Partition refinements are guided by the optimal second-stage dual vectors … Read more

    A Bundle Method for Exploiting Additive Structure in Difficult Optimization Problems

  • Welington de Oliveira
  • Jonathan Eckstein
    • Categories Convex Optimization, Nonsmooth Optimization

    This paper describes a bundle method for (approximately) minimizing complicated nonsmooth convex functions with additive structure, with the primary goal of computing bounds on the solution values of difficult optimization problems such as stochastic integer programs. The method combines features that have appeared in previously proposed bundle methods, but not in the particular configuration we … Read more

    Probabilistic optimization via approximate p-efficient points and bundle methods

  • V. Berge
  • Welington de Oliveira
  • Claudia Sagastizábal
  • Wim van Ackooij
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming

    For problems when decisions are taken prior to observing the realization of underlying random events, probabilistic constraints are an important modelling tool if reliability is a concern. A key concept to numerically dealing with probabilistic constraints is that of p-efficient points. By adopting a dual point of view, we develop a solution framework that includes … Read more

    A strongly convergent proximal bundle method for convex minimization in Hilbert spaces

  • Yunier Bello-Cruz
  • Welington de Oliveira
  • Wim van Ackooij
    • Categories Convex and Nonsmooth Optimization

    A key procedure in proximal bundle methods for convex minimization problems is the definition of stability centers, which are points generated by the iterative process that successfully decrease the objective function. In this paper we study a different stability-center classification rule for proximal bundle methods. We show that the proposed bundle variant has three particularly … Read more

    Bundle methods in the XXIst century: A bird’s-eye view

  • Welington de Oliveira
  • Claudia Sagastizábal
    • Categories Convex Optimization Tags , ,

    Bundle methods are often the algorithms of choice for nonsmooth convex optimization, especially if accuracy in the solution and reliability are a concern. We review several algorithms based on the bundle methodology that have been developed recently and that, unlike their forerunner variants, have the ability to provide exact solutions even if most of the … Read more