libDIPS – discretization-based semi-infinite and bilevel programming solvers

Abstract We consider several hierarchical optimization problems: (generalized) semi-infinite and existence-constrained semi-infinite programs, minmax, and bilevel programs. Multiple adaptive discretization-based algorithms have been published for these problem classes in recent decades. However, rigorous numerical performance comparisons between these algorithms are lacking. Indeed, if numerical comparisons are provided at all, they typically compare a small selection of algorithms on small test sets, across different platforms, and with various subsolvers required during the solution. Additionally, some algorithms have parameters that impede a fair comparison. Our contribution is threefold: i) We present an open-source software called libDIPS (Discretization-based semi-Infinite and bilevel Programming Solvers), which implements multiple adaptive discretization-based solvers. The primary benefit of libDIPS is that it enables users to flexibly switch between the implemented solvers within a single problem class and switch between the available subsolvers. ii) We compile an extensive library of test problems for the (generalized) semi-infinite, minmax, and bilevel problem classes, which, in total, contains over 600 problem instances. Our set includes eight merged test sets and additional problem instances from over 80 literature sources. iii) We compare the solvers numerically using our library of test problems and identify tradeoffs in the parameter tuning.