Applying quantifier elimination to problems in simulation and optimization:
Abstract: "We present a highly optimized method for the elimination of linear variables from a boolean combination of polynomial equations and inequalities. In contrast to the basic method described in [Loos & Weispfenning] the practical applicability of the present method goes far beyond t...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Passau
1996
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| Series: | MIP / Universität Passau, Fakultät für Mathematik und Informatik
1996,07 |
| Subjects: | |
| Summary: | Abstract: "We present a highly optimized method for the elimination of linear variables from a boolean combination of polynomial equations and inequalities. In contrast to the basic method described in [Loos & Weispfenning] the practical applicability of the present method goes far beyond the more academic examples presented in [Loos & Weispfenning]. The optimization is achieved by various strategies to prune superfluous branches in the elimination tree constructed by the method. The main application concern the simulation of large networks of (electric, mechanical or hydraulic) components, whose characteristic curves are with piecewise linear in the variables to be eliminated. A typical goal in technical applications is to determine admissible ranges for certain variables from given ranges of other variables. By keeping certain characteristics of the components parametric, the elimination result can then be used to detect malfunction of certain components solely from the output behaviour of the network. The algorithms are currently used in a commercial software system for industrial applications. Moreover, we extend the elimination method for parametric linear programming in [Weispfenning 2] to the non-convex case by allowing arbitrary and-or combinations of parametric linear inequalities as constraints. We present a new strategy for finding smaller elimination sets and thus smaller elimination trees for parametric linear programming. Some benchmark examples from the NETLIB library of LP problems show the significance of this strategy even for convex linear programming problems." |
| Physical Description: | 22, 4 S. |
Staff View
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| 520 | 3 | |a Abstract: "We present a highly optimized method for the elimination of linear variables from a boolean combination of polynomial equations and inequalities. In contrast to the basic method described in [Loos & Weispfenning] the practical applicability of the present method goes far beyond the more academic examples presented in [Loos & Weispfenning]. The optimization is achieved by various strategies to prune superfluous branches in the elimination tree constructed by the method. The main application concern the simulation of large networks of (electric, mechanical or hydraulic) components, whose characteristic curves are with piecewise linear in the variables to be eliminated. A typical goal in technical applications is to determine admissible ranges for certain variables from given ranges of other variables. By keeping certain characteristics of the components parametric, the elimination result can then be used to detect malfunction of certain components solely from the output behaviour of the network. The algorithms are currently used in a commercial software system for industrial applications. Moreover, we extend the elimination method for parametric linear programming in [Weispfenning 2] to the non-convex case by allowing arbitrary and-or combinations of parametric linear inequalities as constraints. We present a new strategy for finding smaller elimination sets and thus smaller elimination trees for parametric linear programming. Some benchmark examples from the NETLIB library of LP problems show the significance of this strategy even for convex linear programming problems." | |
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| id | DE-604.BV010769323 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:04:59Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007191790 |
| oclc_num | 36067058 |
| open_access_boolean | |
| owner | DE-154 DE-739 DE-12 DE-91G DE-BY-TUM DE-384 DE-634 |
| owner_facet | DE-154 DE-739 DE-12 DE-91G DE-BY-TUM DE-384 DE-634 |
| physical | 22, 4 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| record_format | marc |
| series2 | MIP / Universität Passau, Fakultät für Mathematik und Informatik |
| spelling | Weispfenning, Volker 1944- Verfasser (DE-588)108063550 aut Applying quantifier elimination to problems in simulation and optimization V. Weispfenning Passau 1996 22, 4 S. txt rdacontent n rdamedia nc rdacarrier MIP / Universität Passau, Fakultät für Mathematik und Informatik 1996,07 Abstract: "We present a highly optimized method for the elimination of linear variables from a boolean combination of polynomial equations and inequalities. In contrast to the basic method described in [Loos & Weispfenning] the practical applicability of the present method goes far beyond the more academic examples presented in [Loos & Weispfenning]. The optimization is achieved by various strategies to prune superfluous branches in the elimination tree constructed by the method. The main application concern the simulation of large networks of (electric, mechanical or hydraulic) components, whose characteristic curves are with piecewise linear in the variables to be eliminated. A typical goal in technical applications is to determine admissible ranges for certain variables from given ranges of other variables. By keeping certain characteristics of the components parametric, the elimination result can then be used to detect malfunction of certain components solely from the output behaviour of the network. The algorithms are currently used in a commercial software system for industrial applications. Moreover, we extend the elimination method for parametric linear programming in [Weispfenning 2] to the non-convex case by allowing arbitrary and-or combinations of parametric linear inequalities as constraints. We present a new strategy for finding smaller elimination sets and thus smaller elimination trees for parametric linear programming. Some benchmark examples from the NETLIB library of LP problems show the significance of this strategy even for convex linear programming problems." Algebra, Boolean Elimination Linear programming Simulation methods Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 s Informatik (DE-588)4026894-9 s Mathematik (DE-588)4037944-9 s DE-604 Universität Passau, Fakultät für Mathematik und Informatik MIP 1996,07 (DE-604)BV000905393 1996,07 |
| spellingShingle | Weispfenning, Volker 1944- Applying quantifier elimination to problems in simulation and optimization Algebra, Boolean Elimination Linear programming Simulation methods Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4026894-9 (DE-588)4037944-9 |
| title | Applying quantifier elimination to problems in simulation and optimization |
| title_auth | Applying quantifier elimination to problems in simulation and optimization |
| title_exact_search | Applying quantifier elimination to problems in simulation and optimization |
| title_full | Applying quantifier elimination to problems in simulation and optimization V. Weispfenning |
| title_fullStr | Applying quantifier elimination to problems in simulation and optimization V. Weispfenning |
| title_full_unstemmed | Applying quantifier elimination to problems in simulation and optimization V. Weispfenning |
| title_short | Applying quantifier elimination to problems in simulation and optimization |
| title_sort | applying quantifier elimination to problems in simulation and optimization |
| topic | Algebra, Boolean Elimination Linear programming Simulation methods Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Algebra, Boolean Elimination Linear programming Simulation methods Theoretische Informatik Informatik Mathematik |
| volume_link | (DE-604)BV000905393 |
| work_keys_str_mv | AT weispfenningvolker applyingquantifiereliminationtoproblemsinsimulationandoptimization |