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 … Read more

Adaptive discretization-based algorithms for semi-infinite programs with unbounded variables

The proof of convergence of adaptive discretization-based algorithms for semi-infinite programs (SIPs) usually relies on compact host sets for the upper- and lower-level variables. This assumption is violated in some applications, and we show that indeed convergence problems can arise when discretization-based algorithms are applied to SIPs with unbounded variables. To mitigate these convergence problems, … Read more

An Adaptive Discretization MINLP Algorithm for Optimal Synthesis of Decentralized Energy Supply Systems

Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs and … Read more

WASP: a Wavelet Adaptive Solver for boundary value Problems – Short Reference Manual

This is a short guide to use the Matlab package WASP designed for the numerical solution of two-point linear boundary value problems that arise typically in linear quadratic optimal control. The method relies upon an adaptive computation of discretization based on a wavelet analysis. On a given refined grid, finite differences of various order are … Read more