proximal bundle method

A Stabilised Scenario Decomposition Algorithm Applied to Stochastic Unit Commitment Problems

  • Andreas Grothey
  • Kenneth McKinnon
  • Tim Schulze
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , , ,

    In recent years the expansion of energy supplies from volatile renewable sources has triggered an increased interest in stochastic optimization models for hydro-thermal unit commitment. Several studies have modelled this as a two-stage or multi-stage stochastic mixed-integer optimization problem. Solving such problems directly is computationally intractable for large instances, and alternative approaches are required. In … Read more

    A doubly stabilized bundle method for nonsmooth convex optimization

  • Welington de Oliveira
  • Mikhail V. Solodov
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We propose a bundle method for minimizing nonsmooth convex functions that combines both the level and the proximal stabilizations. Most bundle algorithms use a cutting-plane model of the objective function to formulate a subproblem whose solution gives the next iterate. Proximal bundle methods employ the model in the objective function of the subproblem, while level … Read more

    Inexact Dynamic Bundle Methods

  • Krzysztof C. Kiwiel
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , ,

    We give a proximal bundle method for minimizing a convex function $f$ over $\mathbb{R}_+^n$. It requires evaluating $f$ and its subgradients with a possibly unknown accuracy $\epsilon\ge0$, and maintains a set of free variables $I$ to simplify its prox subproblems. The method asymptotically finds points that are $\epsilon$-optimal. In Lagrangian relaxation of convex programs, it … Read more

    Bundle Methods for Convex Minimization with Partially Inexact Oracles

  • Krzysztof C. Kiwiel
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , ,

    Recently the proximal bundle method for minimizing a convex function has been extended to an inexact oracle that delivers function and subgradient values of unknown accuracy. We adapt this method to a partially inexact oracle that becomes exact only when an objective target level for a descent step is met. In Lagrangian relaxation, such oracles … Read more