adjustable robustness

On the Relation Between Affinely Adjustable Robust Linear Complementarity and Mixed-Integer Linear Feasibility Problems

  • Christian Biefel
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities Tags , , ,

    We consider adjustable robust linear complementarity problems and extend the results of Biefel et al.~(2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an adjustable robust solution of a given linear complementarity problem is equivalent to solving a properly chosen mixed-integer linear feasibility problem. Article … Read more

    Affinely Adjustable Robust Linear Complementarity Problems

  • Christian Biefel
  • Frauke Liers
  • Martin Schmidt
  • Jan Hendrik Rolfes
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Robust Optimization Tags , , , ,

    Linear complementarity problems are a powerful tool for modeling many practically relevant situations such as market equilibria. They also connect many sub-areas of mathematics like game theory, optimization, and matrix theory. Despite their close relation to optimization, the protection of LCPs against uncertainties – especially in the sense of robust optimization – is still in … Read more