A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities

Journal article


Publication Details

Author(s): Schmidt M, Sirvent M, Wollner W
Journal: Mathematical Programming
Publication year: 2018
ISSN: 0025-5610
Language: English


Abstract


Many mixed-integer optimization problems are constrained by nonlinear functions that do not possess desirable analytical properties like convexity or factorability or cannot even be evaluated exactly. This is, e.g., the case for problems constrained by differential equations or for models that rely on black-box simulation runs. For these problem classes, we present, analyze, and test algorithms that solve mixed-integer problems with only Lipschitz continuous nonlinearities. Our theoretical results depend on the assumptions made on the (in)exactness of function evaluations and on the knowledge of Lipschitz constants. If Lipschitz constants are known, we prove finite termination at approximate globally optimal points both for the case of exact and inexact function evaluations. If only approximate Lipschitz constants are known, we prove finite termination and derive additional conditions under which infeasibility can be detected. A computational study for gas transport problems and an academic case study show the applicability of our algorithms to real-world problems and how different assumptions on the constraint functions up- or downgrade the practical performance of the methods.


FAU Authors / FAU Editors

Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen
Sirvent, Mathias
Economics - Discrete Optimization - Mathematics (EDOM)


External institutions
Technische Universität Darmstadt


How to cite

APA:
Schmidt, M., Sirvent, M., & Wollner, W. (2018). A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities. Mathematical Programming. https://dx.doi.org/10.1007/s10107-018-1309-x

MLA:
Schmidt, Martin, Mathias Sirvent, and Winnifried Wollner. "A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities." Mathematical Programming (2018).

BibTeX: 

Last updated on 2018-11-08 at 00:24