multilevel optimization

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. While previous contributions focus on the case of perfectly competitive buyers and sellers of gas, our novel framework considers the mathematically more challenging case of 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