Holdings: Incorporating differential equations into mixed-integer programming for gas transport optimization

Incorporating differential equations into mixed-integer programming for gas transport optimization:

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Bibliographic Details
Main Author:	Sirvent, Mathias (Author)
Format:	Thesis Book
Language:	English
Published:	Erlangen FAU University Press 2018
Series:	FAU studies mathematics & physics Band 13
Subjects:	Gastransport > Gasversorgung Gemischt-ganzzahlige Optimierung Dekomposition Gastransportoptimierung Konvexe Optimierung Nichtkonvexe Optimierung Nichtlineare Optimierung Hochschulschrift
Online Access:	Vollte4xt Volltext Volltext Volltext Inhaltsverzeichnis
Physical Description:	148 Seiten Diagramme, Karten 24 cm, 388 g
ISBN:	9783961471133 3961471134
DOI:	10.25593/978-3-96147-114-0

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MARC


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Record in the Search Index

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adam_text	C ONTENTS A CK NOW LEDGEM EN TS 1 Z USAM M ENFASSUNG 3 A B STRA CT 5 LIST O F F IGURES 8 LIST O F T ABLES 9 1 IN TROD U CTION 13 1.1 THE TITLE OF THIS T H E S I S .......................................................... 13 1.2 CHALLENGES AND GUIDELINES . ...................................................... 14 1.3 SCIENTIFIC CONTRIBUTION AND R E SU LTS........................................ 15 1.4 INCORPORATION OF JOINT WORK WITH OTHER A UTHORS .................. 16 1.5 O RG A N IZ A TIO N ............................................................................ 16 2 L ITERATURE SURVEY: B ASIC C ON CEP TS 19 2.1 COMPUTATIONAL C O M P LE X ITY .................................................... 19 2.2 LINEAR PROGRAM M ING .............................. 20 2.3 MIXED-INTEGER LINEAR PROGRAMMING........................................ 21 2.4 MIXED-INTEGER NONLINEAR PROGRAM M ING.................................. 23 3 G AS T RANSPORT O P TIM IZATION 27 3.1 THE GERMAN ENERGY IN D U S TRY .............................. 28 3.2 MODELING GAS N E TW O RK S.......................................................... 30 3.2.1 N O D E S ............................................................... 31 3.2.2 A R C S ............................................................................... 32 3.2.3 S U M M A RY ...................................................................... 39 3.3 LITERATURE SURVEY: SOLVING GAS TRANSPORT OPTIMIZATION PROB LEMS ........................................................................................... 39 4 D ECO M P O SITIO N M ETH O D S FOR M IXED -IN TEGER N ONLIN EAR P ROGRAM S 43 4.1 PROBLEM S TATEM EN T .............................................................. 44 4.1.1 GENERAL MIXED-INTEGER NONLINEAR P RO G RAM ............... 44 4.1.2 REFORMULATED MIXED-INTEGER NONLINEAR PROGRAM . . 44 4.2 THE A SSUM PTIONS ............... 47 4.3 BASIC ALGORITHMIC FRAM EW ORK ............................................ 48 4.4 THE CASE OF STRICTLY MONOTONIE AND STRICTLY CONCAVE OR CONVEX FUNCTIONS ................................................................. 51 4.4.1 DERIVATION OF THE A LGORITHM ................................... 51 4.4.2 CONVERGENCE R E S U LTS .................................................... 56 4.5 THE CASE OF LIPSCHITZ CONTINUOUS FUNCTIONS AND EXACT FUNC TION EVALUATIONS ....................................................................... 62 4.5.1 DERIVATION OF THE A LGORITHM ........................................ 62 4.5.2 CONVERGENCE R E S U LTS .................................................... 68 4.6 THE CASE OF LIPSCHITZ CONTINUOUS FUNCTIONS AND INEXACT FUNCTION EVALUATIONS . . ............................................................. 72 4.6.1 DERIVATION OF THE A LGORITHM ........................................ 72 4.6.2 CONVERGENCE R E S U LTS .............................................. ... . 75 4.7 LITERATURE SURVEY: RELATED A LGORITHM S ............................. 78 4.8 FURTHER R E M A RK S .................................................................. 80 4.8.1 ALGORITHMIC DETAILS ............ ..................... . 80 4.8.2 LIMITATIONS AND E X TEN SIO N S........................................ 82 4.9 APPLICATION TO STATIONARY GAS TRANSPORT OPTIMIZATION . . . 84 4.9.1 OBJECTIVE F U N CTIO N ....................................................... 85 4.9.2 STATIONARY PIPE M ODEL................................................. 85 4.9.3 NUMERICAL R E S U LTS ....................................................... 89 5 IN STAN TAN EOU S C ONTROL FOR P D E -C O N STRA IN ED M IXED- IN TEGER PROGRAM S 103 5.1 PROBLEM STATEMENT AND DERIVATION OF THE ALGORITHM .... 104 5.2 LITERATURE SURVEY: INSTANTANEOUS C O N TR O L....................... 105 5.3 FURTHER R E M A RK S .................................................................. 106 5.4 APPLICATION TO TRANSIENT GAS TRANSPORT OPTIMIZATION . . . 106 5.4.1 OBJECTIVE F U N CTIO N ....................................................... 107 5.4.2 TRANSIENT PIPE M O D E L ................................................. 109 5.4.3 NUMERICAL R E S U LTS ....................................................... 120 6 SUM M ARY AND OU TLOOK 129 B IB LIOGRAP H Y 131
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spelling	Sirvent, Mathias Verfasser aut Incorporating differential equations into mixed-integer programming for gas transport optimization Mathias Sirvent Erlangen FAU University Press 2018 148 Seiten Diagramme, Karten 24 cm, 388 g txt rdacontent n rdamedia nc rdacarrier FAU studies mathematics & physics Band 13 Dissertation Friedrich-Alexander-Universität Erlangen-Nürnberg 2018 Gastransport Gasversorgung (DE-588)4500861-9 gnd rswk-swf Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd rswk-swf Dekomposition Gastransportoptimierung Gemischt-ganzzahlige Optimierung Konvexe Optimierung Nichtkonvexe Optimierung Nichtlineare Optimierung (DE-588)4113937-9 Hochschulschrift gnd-content Gastransport Gasversorgung (DE-588)4500861-9 s Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 s DE-604 FAU University Press ein Imprint der Universität Erlangen-Nürnberg Universitätsbibliothek (DE-588)1068111240 pbl Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:29-opus4-98628 978-3-96147-114-0 FAU studies mathematics & physics Band 13 (DE-604)BV041186292 13 http://d-nb.info/1166435687/04 Langzeitarchivierung Nationalbibliothek kostenfrei Vollte4xt http://nbn-resolving.org/urn:nbn:de:bvb:29-opus4-98628 Resolving-System kostenfrei Volltext https://doi.org/10.25593/978-3-96147-114-0 Resolving-System kostenfrei Volltext https://open.fau.de/handle/openfau/9862 Verlag kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030595789&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Sirvent, Mathias Incorporating differential equations into mixed-integer programming for gas transport optimization FAU studies mathematics & physics Gastransport Gasversorgung (DE-588)4500861-9 gnd Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd
subject_GND	(DE-588)4500861-9 (DE-588)4156566-6 (DE-588)4113937-9
title	Incorporating differential equations into mixed-integer programming for gas transport optimization
title_auth	Incorporating differential equations into mixed-integer programming for gas transport optimization
title_exact_search	Incorporating differential equations into mixed-integer programming for gas transport optimization
title_full	Incorporating differential equations into mixed-integer programming for gas transport optimization Mathias Sirvent
title_fullStr	Incorporating differential equations into mixed-integer programming for gas transport optimization Mathias Sirvent
title_full_unstemmed	Incorporating differential equations into mixed-integer programming for gas transport optimization Mathias Sirvent
title_short	Incorporating differential equations into mixed-integer programming for gas transport optimization
title_sort	incorporating differential equations into mixed integer programming for gas transport optimization
topic	Gastransport Gasversorgung (DE-588)4500861-9 gnd Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd
topic_facet	Gastransport Gasversorgung Gemischt-ganzzahlige Optimierung Hochschulschrift
url	http://d-nb.info/1166435687/04 http://nbn-resolving.org/urn:nbn:de:bvb:29-opus4-98628 https://doi.org/10.25593/978-3-96147-114-0 https://open.fau.de/handle/openfau/9862 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030595789&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV041186292
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