A decomposition method for MINLPs with Lipschitz continuous nonlinearities
| Autor: | Mathias Sirvent, Winnifried Wollner, Martin Schmidt |
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| Rok vydání: | 2018 |
| Předmět: |
Imagination
021103 operations research Optimization problem Differential equation General Mathematics media_common.quotation_subject Numerical analysis 0211 other engineering and technologies 010103 numerical & computational mathematics 02 engineering and technology Lipschitz continuity 01 natural sciences Convexity Nonlinear system Applied mathematics Decomposition method (constraint satisfaction) 0101 mathematics Software Mathematics media_common |
| Zdroj: | Mathematical Programming. 178:449-483 |
| ISSN: | 1436-4646 0025-5610 |
| DOI: | 10.1007/s10107-018-1309-x |
| Popis: | 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 many 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 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. |
| Databáze: | OpenAIRE |
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