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Adaptive discretization algorithms for unbounded semi-infinite programs

Daniel Jungen(daniel.jungen***at***avt.rwth-aachen.de)
Hatim Djelassi(hatim.djelassi***at***uliege.be)
Alexander Mitsos(amitsos***at***alum.mit.edu)

Abstract: 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 host sets. To mitigate these convergence problems, we first examine the assumptions underlying the algorithm proposed in [Mitsos. Optimization, 2011], which uses the algorithm proposed by [Blankenship and Falk. JOTA, 1976] as the lower-bounding procedure. We give sharper, slightly relaxed, assumptions with which we achieve the same convergence guarantees. We show that the convergence guarantees also hold for certain SIPs with unbounded host sets based on these sharpened assumptions. However, convergence guarantees cannot be given for SIPs with unbounded host sets in the general case. For these cases, we propose additional assumptions which restore the convergence guarantee. Using these additional assumptions, we present numerical case studies with unbounded host sets. Finally, we review which applications are tractable with the proposed additional assumptions.

Keywords: semi-infinite programming, unbounded, adaptive discretization

Category 1: Global Optimization (Other )

Citation: October 2021, Process Systems Engineering (AVT.SVT), RWTH Aachen University, Forckenbeckstraße 51, Aachen 52074, Germany

Download: [PDF]

Entry Submitted: 10/11/2021
Entry Accepted: 11/01/2021
Entry Last Modified: 10/11/2021

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