libDIPS — Discretization-Based Semi-Infinite and Bilevel Programming Solvers

We consider several hierarchical optimization programs: (generalized) semi-infinite and existence-constrained semi-infinite programs, minmax, and bilevel programs.
Multiple adaptive discretization-based algorithms have been published for these program classes in recent decades.
However, rigorous numerical performance comparisons between these algorithms are lacking.
Indeed, if numerical comparisons are provided at all, they usually compare a small selection of algorithms on small benchmark test sets, on different platforms, and with different subsolvers, which are needed during the solution.
Additionally, some algorithms have hyperparameters, which impedes a fair comparison.
Our contribution is threefold:

  1. We present an open-source software called libDIPS (Discretization-Based Semi-Infinite and Bilevel Programming Solvers), which implements multiple adaptive discretization-based solvers.
    The main benefit of libDIPS is that it lets the user flexibly change between the implemented solvers within one program class and switch between the available subsolvers.
  2.  We compile an extensive benchmark test set for (generalized) semi-infinite, minmax, and bilevel programs, which, in total, contains over 600 problem instances.
    Our set includes eight merged test sets and additional problem instances from over 80 literature sources.
  3.  We compare the solvers numerically on our benchmark test set and identify tradeoffs in the hyperparameters tuning.



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