Nondifferentiable Optimization and Polynomial Problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1998
|
| Schriftenreihe: | Nonconvex Optimization and Its Applications
24 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P. |
| Beschreibung: | 1 Online-Ressource (XVII, 396 p) |
| ISBN: | 9781475760156 9781441947925 |
| ISSN: | 1571-568X |
| DOI: | 10.1007/978-1-4757-6015-6 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421679 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1998 |||| o||u| ||||||eng d | ||
| 020 | |a 9781475760156 |c Online |9 978-1-4757-6015-6 | ||
| 020 | |a 9781441947925 |c Print |9 978-1-4419-4792-5 | ||
| 024 | 7 | |a 10.1007/978-1-4757-6015-6 |2 doi | |
| 035 | |a (OCoLC)863994465 | ||
| 035 | |a (DE-599)BVBBV042421679 | ||
| 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 519.6 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Shor, Naum Z. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nondifferentiable Optimization and Polynomial Problems |c by Naum Z. Shor |
| 264 | 1 | |a Boston, MA |b Springer US |c 1998 | |
| 300 | |a 1 Online-Ressource (XVII, 396 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Nonconvex Optimization and Its Applications |v 24 |x 1571-568X | |
| 500 | |a Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P. | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Electronic data processing | |
| 650 | 4 | |a Combinatorics | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Engineering | |
| 650 | 4 | |a Operations research | |
| 650 | 4 | |a Optimization | |
| 650 | 4 | |a Engineering, general | |
| 650 | 4 | |a Operation Research/Decision Theory | |
| 650 | 4 | |a Numeric Computing | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Ingenieurwissenschaften | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Nichtdifferenzierbare Funktion |0 (DE-588)4326748-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Polynom |0 (DE-588)4046711-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 0 | 1 | |a Polynom |0 (DE-588)4046711-9 |D s |
| 689 | 0 | 2 | |a Nichtdifferenzierbare Funktion |0 (DE-588)4326748-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4757-6015-6 |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:BVB01-027857096 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153095027949568 |
|---|---|
| any_adam_object | |
| author | Shor, Naum Z. |
| author_facet | Shor, Naum Z. |
| author_role | aut |
| author_sort | Shor, Naum Z. |
| author_variant | n z s nz nzs |
| building | Verbundindex |
| bvnumber | BV042421679 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863994465 (DE-599)BVBBV042421679 |
| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-6015-6 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03433nmm a2200613zcb4500</leader><controlfield tag="001">BV042421679</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1998 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781475760156</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4757-6015-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441947925</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4419-4792-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4757-6015-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863994465</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421679</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">519.6</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">Shor, Naum Z.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nondifferentiable Optimization and Polynomial Problems</subfield><subfield code="c">by Naum Z. Shor</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, MA</subfield><subfield code="b">Springer US</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XVII, 396 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="0" ind2=" "><subfield code="a">Nonconvex Optimization and Its Applications</subfield><subfield code="v">24</subfield><subfield code="x">1571-568X</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Electronic data processing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Combinatorics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Engineering</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operations research</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Engineering, general</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">Numeric Computing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ingenieurwissenschaften</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtdifferenzierbare Funktion</subfield><subfield code="0">(DE-588)4326748-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Polynom</subfield><subfield code="0">(DE-588)4046711-9</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="689" ind1="0" 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="0" ind2="1"><subfield code="a">Polynom</subfield><subfield code="0">(DE-588)4046711-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Nichtdifferenzierbare Funktion</subfield><subfield code="0">(DE-588)4326748-8</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="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4757-6015-6</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:BVB01-027857096</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></record></collection> |
| id | DE-604.BV042421679 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475760156 9781441947925 |
| issn | 1571-568X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857096 |
| oclc_num | 863994465 |
| 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 (XVII, 396 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer US |
| record_format | marc |
| series2 | Nonconvex Optimization and Its Applications |
| spelling | Shor, Naum Z. Verfasser aut Nondifferentiable Optimization and Polynomial Problems by Naum Z. Shor Boston, MA Springer US 1998 1 Online-Ressource (XVII, 396 p) txt rdacontent c rdamedia cr rdacarrier Nonconvex Optimization and Its Applications 24 1571-568X Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P. Mathematics Electronic data processing Combinatorics Mathematical optimization Engineering Operations research Optimization Engineering, general Operation Research/Decision Theory Numeric Computing Datenverarbeitung Ingenieurwissenschaften Mathematik Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s Polynom (DE-588)4046711-9 s Nichtdifferenzierbare Funktion (DE-588)4326748-8 s 1\p DE-604 https://doi.org/10.1007/978-1-4757-6015-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shor, Naum Z. Nondifferentiable Optimization and Polynomial Problems Mathematics Electronic data processing Combinatorics Mathematical optimization Engineering Operations research Optimization Engineering, general Operation Research/Decision Theory Numeric Computing Datenverarbeitung Ingenieurwissenschaften Mathematik Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd Polynom (DE-588)4046711-9 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4326748-8 (DE-588)4046711-9 (DE-588)4043664-0 |
| title | Nondifferentiable Optimization and Polynomial Problems |
| title_auth | Nondifferentiable Optimization and Polynomial Problems |
| title_exact_search | Nondifferentiable Optimization and Polynomial Problems |
| title_full | Nondifferentiable Optimization and Polynomial Problems by Naum Z. Shor |
| title_fullStr | Nondifferentiable Optimization and Polynomial Problems by Naum Z. Shor |
| title_full_unstemmed | Nondifferentiable Optimization and Polynomial Problems by Naum Z. Shor |
| title_short | Nondifferentiable Optimization and Polynomial Problems |
| title_sort | nondifferentiable optimization and polynomial problems |
| topic | Mathematics Electronic data processing Combinatorics Mathematical optimization Engineering Operations research Optimization Engineering, general Operation Research/Decision Theory Numeric Computing Datenverarbeitung Ingenieurwissenschaften Mathematik Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd Polynom (DE-588)4046711-9 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Mathematics Electronic data processing Combinatorics Mathematical optimization Engineering Operations research Optimization Engineering, general Operation Research/Decision Theory Numeric Computing Datenverarbeitung Ingenieurwissenschaften Mathematik Nichtdifferenzierbare Funktion Polynom Optimierung |
| url | https://doi.org/10.1007/978-1-4757-6015-6 |
| work_keys_str_mv | AT shornaumz nondifferentiableoptimizationandpolynomialproblems |