Optimization: Algorithms and Consistent Approximations
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1997
|
| Series: | Applied Mathematical Sciences
124 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This book deals with optimality conditions, algorithms, and discretization techniques for nonlinear programming, semi-infinite optimization, and optimal control problems. The unifying thread in the presentation consists of an abstract theory, within which optimality conditions are expressed in the form of zeros of optimality junctions, algorithms are characterized by point-to-set iteration maps, and all the numerical approximations required in the solution of semi-infinite optimization and optimal control problems are treated within the context of consistent approximations and algorithm implementation techniques. Traditionally, necessary optimality conditions for optimization problems are presented in Lagrange, F. John, or Karush-Kuhn-Tucker multiplier forms, with gradients used for smooth problems and subgradients for nonsmooth problems. We present these classical optimality conditions and show that they are satisfied at a point if and only if this point is a zero of an upper semicontinuous optimality junction. The use of optimality functions has several advantages. First, optimality functions can be used in an abstract study of optimization algorithms. Second, many optimization algorithms can be shown to use search directions that are obtained in evaluating optimality functions, thus establishing a clear relationship between optimality conditions and algorithms. Third, establishing optimality conditions for highly complex problems, such as optimal control problems with control and trajectory constraints, is much easier in terms of optimality functions than in the classical manner. In addition, the relationship between optimality conditions for finite-dimensional problems and semi-infinite optimization and optimal control problems becomes transparent |
| Physical Description: | 1 Online-Ressource (XX, 782 p) |
| ISBN: | 9781461206637 9781461268611 |
| DOI: | 10.1007/978-1-4612-0663-7 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042419587 | ||
| 003 | DE-604 | ||
| 005 | 20200707 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1997 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461206637 |c Online |9 978-1-4612-0663-7 | ||
| 020 | |a 9781461268611 |c Print |9 978-1-4612-6861-1 | ||
| 024 | 7 | |a 10.1007/978-1-4612-0663-7 |2 doi | |
| 035 | |a (OCoLC)863757508 | ||
| 035 | |a (DE-599)BVBBV042419587 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.64 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Polak, Elijah |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Optimization |b Algorithms and Consistent Approximations |c by Elijah Polak |
| 264 | 1 | |a New York, NY |b Springer New York |c 1997 | |
| 300 | |a 1 Online-Ressource (XX, 782 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Applied Mathematical Sciences |v 124 | |
| 500 | |a This book deals with optimality conditions, algorithms, and discretization techniques for nonlinear programming, semi-infinite optimization, and optimal control problems. The unifying thread in the presentation consists of an abstract theory, within which optimality conditions are expressed in the form of zeros of optimality junctions, algorithms are characterized by point-to-set iteration maps, and all the numerical approximations required in the solution of semi-infinite optimization and optimal control problems are treated within the context of consistent approximations and algorithm implementation techniques. Traditionally, necessary optimality conditions for optimization problems are presented in Lagrange, F. John, or Karush-Kuhn-Tucker multiplier forms, with gradients used for smooth problems and subgradients for nonsmooth problems. We present these classical optimality conditions and show that they are satisfied at a point if and only if this point is a zero of an upper semicontinuous optimality junction. The use of optimality functions has several advantages. First, optimality functions can be used in an abstract study of optimization algorithms. Second, many optimization algorithms can be shown to use search directions that are obtained in evaluating optimality functions, thus establishing a clear relationship between optimality conditions and algorithms. Third, establishing optimality conditions for highly complex problems, such as optimal control problems with control and trajectory constraints, is much easier in terms of optimality functions than in the classical manner. In addition, the relationship between optimality conditions for finite-dimensional problems and semi-infinite optimization and optimal control problems becomes transparent | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Systems theory | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Operations research | |
| 650 | 4 | |a Calculus of Variations and Optimal Control; Optimization | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Systems Theory, Control | |
| 650 | 4 | |a Operation Research/Decision Theory | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Semiinfinite Optimierung |0 (DE-588)4137036-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Semiinfinite Optimierung |0 (DE-588)4137036-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 689 | 3 | 0 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |D s |
| 689 | 3 | |8 4\p |5 DE-604 | |
| 830 | 0 | |a Applied Mathematical Sciences |v 124 |w (DE-604)BV040244599 |9 124 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-0663-7 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027855004 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 4\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153090417360896 |
|---|---|
| any_adam_object | |
| author | Polak, Elijah |
| author_facet | Polak, Elijah |
| author_role | aut |
| author_sort | Polak, Elijah |
| author_variant | e p ep |
| building | Verbundindex |
| bvnumber | BV042419587 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863757508 (DE-599)BVBBV042419587 |
| dewey-full | 515.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.64 |
| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0663-7 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04361nmm a2200673zcb4500</leader><controlfield tag="001">BV042419587</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200707 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1997 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461206637</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-0663-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461268611</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4612-6861-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-0663-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863757508</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042419587</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.64</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Polak, Elijah</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Optimization</subfield><subfield code="b">Algorithms and Consistent Approximations</subfield><subfield code="c">by Elijah Polak</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XX, 782 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Applied Mathematical Sciences</subfield><subfield code="v">124</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book deals with optimality conditions, algorithms, and discretization techniques for nonlinear programming, semi-infinite optimization, and optimal control problems. The unifying thread in the presentation consists of an abstract theory, within which optimality conditions are expressed in the form of zeros of optimality junctions, algorithms are characterized by point-to-set iteration maps, and all the numerical approximations required in the solution of semi-infinite optimization and optimal control problems are treated within the context of consistent approximations and algorithm implementation techniques. Traditionally, necessary optimality conditions for optimization problems are presented in Lagrange, F. John, or Karush-Kuhn-Tucker multiplier forms, with gradients used for smooth problems and subgradients for nonsmooth problems. We present these classical optimality conditions and show that they are satisfied at a point if and only if this point is a zero of an upper semicontinuous optimality junction. The use of optimality functions has several advantages. First, optimality functions can be used in an abstract study of optimization algorithms. Second, many optimization algorithms can be shown to use search directions that are obtained in evaluating optimality functions, thus establishing a clear relationship between optimality conditions and algorithms. Third, establishing optimality conditions for highly complex problems, such as optimal control problems with control and trajectory constraints, is much easier in terms of optimality functions than in the classical manner. In addition, the relationship between optimality conditions for finite-dimensional problems and semi-infinite optimization and optimal control problems becomes transparent</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Systems theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operations research</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Calculus of Variations and Optimal Control; Optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Applications of Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Systems Theory, Control</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operation Research/Decision Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Semiinfinite Optimierung</subfield><subfield code="0">(DE-588)4137036-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Optimierung</subfield><subfield code="0">(DE-588)4128192-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Optimierung</subfield><subfield code="0">(DE-588)4043664-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Optimale Kontrolle</subfield><subfield code="0">(DE-588)4121428-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Semiinfinite Optimierung</subfield><subfield code="0">(DE-588)4137036-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Optimierung</subfield><subfield code="0">(DE-588)4043664-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Nichtlineare Optimierung</subfield><subfield code="0">(DE-588)4128192-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Optimale Kontrolle</subfield><subfield code="0">(DE-588)4121428-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="8">4\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applied Mathematical Sciences</subfield><subfield code="v">124</subfield><subfield code="w">(DE-604)BV040244599</subfield><subfield code="9">124</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-0663-7</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027855004</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">4\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042419587 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461206637 9781461268611 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855004 |
| oclc_num | 863757508 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XX, 782 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer New York |
| record_format | marc |
| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | Polak, Elijah Verfasser aut Optimization Algorithms and Consistent Approximations by Elijah Polak New York, NY Springer New York 1997 1 Online-Ressource (XX, 782 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 124 This book deals with optimality conditions, algorithms, and discretization techniques for nonlinear programming, semi-infinite optimization, and optimal control problems. The unifying thread in the presentation consists of an abstract theory, within which optimality conditions are expressed in the form of zeros of optimality junctions, algorithms are characterized by point-to-set iteration maps, and all the numerical approximations required in the solution of semi-infinite optimization and optimal control problems are treated within the context of consistent approximations and algorithm implementation techniques. Traditionally, necessary optimality conditions for optimization problems are presented in Lagrange, F. John, or Karush-Kuhn-Tucker multiplier forms, with gradients used for smooth problems and subgradients for nonsmooth problems. We present these classical optimality conditions and show that they are satisfied at a point if and only if this point is a zero of an upper semicontinuous optimality junction. The use of optimality functions has several advantages. First, optimality functions can be used in an abstract study of optimization algorithms. Second, many optimization algorithms can be shown to use search directions that are obtained in evaluating optimality functions, thus establishing a clear relationship between optimality conditions and algorithms. Third, establishing optimality conditions for highly complex problems, such as optimal control problems with control and trajectory constraints, is much easier in terms of optimality functions than in the classical manner. In addition, the relationship between optimality conditions for finite-dimensional problems and semi-infinite optimization and optimal control problems becomes transparent Mathematics Systems theory Mathematical optimization Operations research Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Systems Theory, Control Operation Research/Decision Theory Mathematik Semiinfinite Optimierung (DE-588)4137036-3 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Semiinfinite Optimierung (DE-588)4137036-3 s 1\p DE-604 Optimierung (DE-588)4043664-0 s 2\p DE-604 Nichtlineare Optimierung (DE-588)4128192-5 s 3\p DE-604 Optimale Kontrolle (DE-588)4121428-6 s 4\p DE-604 Applied Mathematical Sciences 124 (DE-604)BV040244599 124 https://doi.org/10.1007/978-1-4612-0663-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Polak, Elijah Optimization Algorithms and Consistent Approximations Applied Mathematical Sciences Mathematics Systems theory Mathematical optimization Operations research Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Systems Theory, Control Operation Research/Decision Theory Mathematik Semiinfinite Optimierung (DE-588)4137036-3 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Optimierung (DE-588)4043664-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4137036-3 (DE-588)4128192-5 (DE-588)4043664-0 (DE-588)4121428-6 |
| title | Optimization Algorithms and Consistent Approximations |
| title_auth | Optimization Algorithms and Consistent Approximations |
| title_exact_search | Optimization Algorithms and Consistent Approximations |
| title_full | Optimization Algorithms and Consistent Approximations by Elijah Polak |
| title_fullStr | Optimization Algorithms and Consistent Approximations by Elijah Polak |
| title_full_unstemmed | Optimization Algorithms and Consistent Approximations by Elijah Polak |
| title_short | Optimization |
| title_sort | optimization algorithms and consistent approximations |
| title_sub | Algorithms and Consistent Approximations |
| topic | Mathematics Systems theory Mathematical optimization Operations research Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Systems Theory, Control Operation Research/Decision Theory Mathematik Semiinfinite Optimierung (DE-588)4137036-3 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Optimierung (DE-588)4043664-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Mathematics Systems theory Mathematical optimization Operations research Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Systems Theory, Control Operation Research/Decision Theory Mathematik Semiinfinite Optimierung Nichtlineare Optimierung Optimierung Optimale Kontrolle |
| url | https://doi.org/10.1007/978-1-4612-0663-7 |
| volume_link | (DE-604)BV040244599 |
| work_keys_str_mv | AT polakelijah optimizationalgorithmsandconsistentapproximations |