Theory of functional connections applied to quadratic and nonlinear programming under equality constraints
This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange multiplier technique. More specifically, two distinct expressions (fu...
Gespeichert in:
| Veröffentlicht in: | arXiv.org |
|---|---|
| Hauptverfasser: | , |
| Format: | Paper |
| Sprache: | Englisch |
| Veröffentlicht: |
Ithaca
Cornell University Library, arXiv.org
25.08.2022
|
| Schlagworte: | |
| ISSN: | 2331-8422 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange multiplier technique. More specifically, two distinct expressions (fully satisfying the equality constraints) are provided, to first solve the constrained quadratic programming problem as an unconstrained one for closed-form solution. Such expressions are derived via using an optimization variable vector, which is called the free vector \(\boldsymbol{g}\) by the Theory of Functional Connections. In the spirit of this Theory, for the equality constrained nonlinear programming problem, its solution is obtained by the Newton's method combining with elimination scheme in optimization. Convergence analysis is supported by a numerical example for the proposed approach. |
|---|---|
| AbstractList | This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange multiplier technique. More specifically, two distinct expressions (fully satisfying the equality constraints) are provided, to first solve the constrained quadratic programming problem as an unconstrained one for closed-form solution. Such expressions are derived via using an optimization variable vector, which is called the free vector \(\boldsymbol{g}\) by the Theory of Functional Connections. In the spirit of this Theory, for the equality constrained nonlinear programming problem, its solution is obtained by the Newton's method combining with elimination scheme in optimization. Convergence analysis is supported by a numerical example for the proposed approach. |
| Author | Mai, Tina Mortari, Daniele |
| Author_xml | – sequence: 1 givenname: Tina surname: Mai fullname: Mai, Tina – sequence: 2 givenname: Daniele surname: Mortari fullname: Mortari, Daniele |
| BookMark | eNotT8tKAzEADKJgrf0AbwHPW_Pe5CjFFxS87L1k86hZtkmbZMX-vevjNMwwzOMGXMYUHQB3GK2Z5Bw96PwVPtdYzQJiCrcXYEEoxY1khFyDVSkDQoiIlnBOF2DoPlzKZ5g89FM0NaSoR2hSjO6XFKiPxzE4C2uCp0nbrGswUEcL5-IxRKczPOa0z_pwCHEPp2hdhm62jqGef5JKzTrEWm7Blddjcat_XILu-anbvDbb95e3zeO20ZyIxhBGkJak5QZTo3zrqZO9Z4IoZhnnjFumJLJSaq6o75nAlgvjW9v3zHlGl-D-L3ZedZpcqbshTXl-VXaEIk4JVkLQb0kRXXA |
| ContentType | Paper |
| Copyright | 2022. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2022. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.48550/arxiv.1910.04917 |
| DatabaseName | ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic (New) ProQuest Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | Publicly Available Content Database Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) Engineering Collection |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: PIMPY name: ProQuest Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2331-8422 |
| Genre | Working Paper/Pre-Print |
| GroupedDBID | 8FE 8FG ABJCF ABUWG AFKRA ALMA_UNASSIGNED_HOLDINGS AZQEC BENPR BGLVJ CCPQU DWQXO FRJ HCIFZ L6V M7S M~E PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| ID | FETCH-LOGICAL-a526-c2420a8275c13c9f7f3e8bf46294d45545d4980d88a593fb461d56cf7dbb4ef43 |
| IEDL.DBID | M7S |
| IngestDate | Mon Jun 30 08:27:40 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a526-c2420a8275c13c9f7f3e8bf46294d45545d4980d88a593fb461d56cf7dbb4ef43 |
| Notes | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| OpenAccessLink | https://www.proquest.com/docview/2305321966?pq-origsite=%requestingapplication% |
| PQID | 2305321966 |
| PQPubID | 2050157 |
| ParticipantIDs | proquest_journals_2305321966 |
| PublicationCentury | 2000 |
| PublicationDate | 20220825 |
| PublicationDateYYYYMMDD | 2022-08-25 |
| PublicationDate_xml | – month: 08 year: 2022 text: 20220825 day: 25 |
| PublicationDecade | 2020 |
| PublicationPlace | Ithaca |
| PublicationPlace_xml | – name: Ithaca |
| PublicationTitle | arXiv.org |
| PublicationYear | 2022 |
| Publisher | Cornell University Library, arXiv.org |
| Publisher_xml | – name: Cornell University Library, arXiv.org |
| SSID | ssj0002672553 |
| Score | 1.8046879 |
| SecondaryResourceType | preprint |
| Snippet | This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of... |
| SourceID | proquest |
| SourceType | Aggregation Database |
| SubjectTerms | Constraints Equality Iterative methods Lagrange multiplier Mathematical analysis Mathematical programming Newton methods Nonlinear programming Optimization Quadratic programming |
| Title | Theory of functional connections applied to quadratic and nonlinear programming under equality constraints |
| URI | https://www.proquest.com/docview/2305321966 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELagBYmJt3iUygNr2sSvOBMSiAoGqgg6lKnyUyoSfSRpBf8e20mBiYXRshRZdu7u8_m7-wC4TlLBmHDXEoUU9dkqFQkXdaIEM0OURD6KBbGJdDjk43GWNwm3sqFVbnxicNR6rnyOvO-gMsXOvBi7WSwjrxrlX1cbCY1t0PZdEpJA3Xv5zrEgljrEjOvHzNC6qy-Kj-m65y4pcc9h40am7LcLDnFlsP_fFR2Adi4WpjgEW2Z2BHYDn1OVx-CtrrmHcwt95KoTflB5VksYlFDU8BNWc7hcCe1_BAXFTMNZ3TxDFLDhbr276AZ9rVkBTV2D-em_VAZ1iao8AaPB_ejuIWpkFSJBEXOHQlAsOEqpSrDKbGqx4dIShjKiiUMXVJOMx5pzQTNsJWGJpkzZVEtJjCX4FLTcSswZgLGV0sbSQSRhCBeS29TBTaQYVVirhJyDzmbnJo1plJOfbbv4e_oS7CFfaxA7U6Yd0KqKlbkCO2pdTcuiC9q398P8uRtO3I3yx6f89Qt1CbkC |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V25TsQwEB1xCipuceMCykDi2E5SIAoOgYAVEltst_IpLRJ7JMv1UfwjY2cXqOi2oIwiWU5mPPNmPDMP4DDJpBASwxJNNffZKh1J9DpRkgrLtKLeiwWyiazRyFut4mEKPse9ML6scmwTg6E2Pe1z5CcIlXmKx0uIs_4g8qxR_nZ1TKFRq8Wt_XjDkK06vblA-R5RenXZPL-ORqwCkeRU4J4YjWVOM66TVBcuc6nNlWOCFswwdK7csCKPTZ5LXqROMZEYLrTLjFLMOpbistMwiyiCFqFS8PE7pUNFhgA9re9Ow6SwE1m-d16PMSaKjxGKj1jRflv84Maulv7ZD1iG2QfZt-UKTNnuKsyHalVdrcFTPVGA9BzxfrlOZxLta3bCQ0VkDa7JsEcGL9J4NddEdg3p1qNBZElGlWnP6LuJ76Qria07TD_8SlXgzhhW69CcxNdtwAzuxG4CiZ1SLlYIAKVluVS5yxBMUy24To1O2BbsjgXVHh38qv0jpe2_Xx_AwnXz_q59d9O43YFF6rsqYjRafBdmhuWL3YM5_TrsVOV-UDIC7QnL9AuJxhDH |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Theory+of+functional+connections+applied+to+quadratic+and+nonlinear+programming+under+equality+constraints&rft.jtitle=arXiv.org&rft.au=Mai%2C+Tina&rft.au=Mortari%2C+Daniele&rft.date=2022-08-25&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.1910.04917 |