Wim van Ackooij

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

    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

    Decomposition algorithm for large-scale two-stage unit-commitment

  • Jérôme Malick
  • Wim van Ackooij
    • Categories Applications - OR and Management Sciences, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    Everyday, electricity generation companies submit a generation schedule to the grid operator for the coming day; computing an optimal schedule is called the unit-commitment problem. Generation companies can also occasionally submit changes to the schedule, that can be seen as intra-daily incomplete recourse actions. In this paper, we propose a two-stage formulation of unit-commitment, wherein … 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

    Level Bundle Methods for Constrained Convex Optimization with Various Oracles

  • Welington de Oliveira
  • Wim van Ackooij
    • Categories Nonsmooth Optimization

    We propose restricted memory level bundle methods for minimizing constrained convex nonsmooth optimization problems whose objective and constraint functions are known through oracles (black-boxes) that might provide inexact information. Our approach is general and covers many instances of inexact oracles, such as upper, lower and on-demand oracles. We show that the proposed level bundle methods … Read more

    Constrained Bundle Methods for Upper Inexact Oracles with Application to Joint Chance Constrained Energy Problems

  • Claudia Sagastizábal
  • Wim van Ackooij
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , ,

    Joint chance constrained problems give rise to many algorithmic challenges. Even in the convex case, i.e., when an appropriate transformation of the probabilistic constraint is a convex function, its cutting-plane linearization is just an approximation, produced by an oracle providing subgradient and function values that can only be evaluated inexactly. As a result, the cutting-plane … Read more