multilevel optimization

Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization

  • Serge Gratton
  • Alena Kopanicakova
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Data Science Algorithms, Nonlinear Optimization Tags , , , , , ,

    Two OFFO (Objective-Function Free Optimization) noise tolerant algorithms are presented that handle bound constraints, inexact gradients and use second-order information when available. The first is a multi-level method exploiting a hierarchical description of the problem and the second is a domain-decomposition method covering the standard addditive Schwarz decompositions. Both are generalizations of the first-order AdaGrad … Read more

    Unboundedness in Bilevel Optimization

  • Bárbara Rodrigues
  • Margarida Carvalho
  • Miguel F. Anjos
  • nsugishita
    • Categories Bilevel Optimization, Nonlinear Optimization Tags , , ,

    Bilevel optimization has garnered growing interest over the past decade. However, little attention has been paid to detecting and dealing with unboundedness in these problems, with most research assuming a bounded high-point relaxation. In this paper, we address unboundedness in bilevel and multilevel optimization by studying its computational complexity. We show that deciding whether an … Read more

    On a Tractable Single-Level Reformulation of a Multilevel Model of the European Entry-Exit Gas Market with Market Power

  • Veronika Grimm
  • Julia Grübel
  • Martin Schmidt
  • Alexandra Schwartz
  • Gregor Zöttl
  • Ann-Kathrin Wiertz
    • Categories Complementarity and Variational Inequalities, Energy Tags , , ,

    We propose a framework that allows to quantitatively analyze the interplay of the different agents involved in gas trade and transport in the context of the European entry-exit system. Previous contributions have focused on the case of perfectly competitive buyers and sellers of gas, which allows to replace the respective market equilibrium problem by a … Read more

    Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training

  • Serge Gratton
  • Alena Kopanicakova
  • Philippe L. Toint
    • Categories Data Science Algorithms, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , ,

    A class of multi-level algorithms for unconstrained nonlinear optimization is presented which does not require the evaluation of the objective function. The class contains the momentum-less AdaGrad method as a particular (single-level) instance. The choice of avoiding the evaluation of the objective function is intended to make the algorithms of the class less sensitive to … Read more