The Lipschitz Properties of the Value Function and the Solution Map to a Parametric Discrete Optimal Control Problem
Motivated by the works of Toan and Kien ( J. Nonlinear Convex Anal. 12 :635–650, 2011 ) and Thuy and Toan ( Acta Math. Vietnam. 43 :175–199, 2018 ) on the stability and the solution sensitivity in parametric discrete optimal control problems, this paper is devoted to the study of the Lipschitz prope...
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| Veröffentlicht in: | Acta mathematica vietnamica 2020-06, Vol.45 (2), p.365-382 |
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| container_title | Acta mathematica vietnamica |
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| creator | Toan, Nguyen Thi Thuy, Le Quang |
| description | Motivated by the works of Toan and Kien (
J. Nonlinear Convex Anal.
12
:635–650,
2011
) and Thuy and Toan (
Acta Math. Vietnam.
43
:175–199,
2018
) on the stability and the solution sensitivity in parametric discrete optimal control problems, this paper is devoted to the study of the Lipschitz property of the value function and the Aubin property of the solution map to a parametric dynamic programming problem with linear constraints. By establishing abstract results on the Lipschitz property of the value function to a parametric programming and the Aubin property of the solution map to a parametric variational inequality, we obtain the Lipschitz property of the value function and the Aubin property of the solution map to a parametric discrete optimal control problem. |
| doi_str_mv | 10.1007/s40306-020-00371-5 |
| format | Article |
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J. Nonlinear Convex Anal.
12
:635–650,
2011
) and Thuy and Toan (
Acta Math. Vietnam.
43
:175–199,
2018
) on the stability and the solution sensitivity in parametric discrete optimal control problems, this paper is devoted to the study of the Lipschitz property of the value function and the Aubin property of the solution map to a parametric dynamic programming problem with linear constraints. By establishing abstract results on the Lipschitz property of the value function to a parametric programming and the Aubin property of the solution map to a parametric variational inequality, we obtain the Lipschitz property of the value function and the Aubin property of the solution map to a parametric discrete optimal control problem.</description><identifier>ISSN: 0251-4184</identifier><identifier>EISSN: 2315-4144</identifier><identifier>DOI: 10.1007/s40306-020-00371-5</identifier><language>eng</language><publisher>Singapore: Springer Singapore</publisher><subject>Control stability ; Dynamic programming ; Mathematics ; Mathematics and Statistics ; Optimal control ; Parameter sensitivity</subject><ispartof>Acta mathematica vietnamica, 2020-06, Vol.45 (2), p.365-382</ispartof><rights>Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2020</rights><rights>Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-399944bc330ac4979d60351d585dc466273699078347480ba817b119fd45d8e63</citedby><cites>FETCH-LOGICAL-c319t-399944bc330ac4979d60351d585dc466273699078347480ba817b119fd45d8e63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40306-020-00371-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40306-020-00371-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Toan, Nguyen Thi</creatorcontrib><creatorcontrib>Thuy, Le Quang</creatorcontrib><title>The Lipschitz Properties of the Value Function and the Solution Map to a Parametric Discrete Optimal Control Problem</title><title>Acta mathematica vietnamica</title><addtitle>Acta Math Vietnam</addtitle><description>Motivated by the works of Toan and Kien (
J. Nonlinear Convex Anal.
12
:635–650,
2011
) and Thuy and Toan (
Acta Math. Vietnam.
43
:175–199,
2018
) on the stability and the solution sensitivity in parametric discrete optimal control problems, this paper is devoted to the study of the Lipschitz property of the value function and the Aubin property of the solution map to a parametric dynamic programming problem with linear constraints. By establishing abstract results on the Lipschitz property of the value function to a parametric programming and the Aubin property of the solution map to a parametric variational inequality, we obtain the Lipschitz property of the value function and the Aubin property of the solution map to a parametric discrete optimal control problem.</description><subject>Control stability</subject><subject>Dynamic programming</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Optimal control</subject><subject>Parameter sensitivity</subject><issn>0251-4184</issn><issn>2315-4144</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9UEFOwzAQtBBIVKUf4GSJc2Ad23F8RIUCUlErUbhajuPQoDQOtnOA1-O2SNw47Wp2ZnZ3ELokcE0AxE1gQKHIIIcMgAqS8RM0ySnhGSOMnaIJ5JykvmTnaBZCWwGhogBR8gmKm63Fy3YIZtvGb7z2brA-tjZg1-CYZm-6Gy1ejL2Jreux7usD_OK68QA86wFHhzVea693NvrW4Ls2GG-jxashtjvd4bnro3fd3r7q7O4CnTW6C3b2W6fodXG_mT9my9XD0_x2mRlKZMyolJKxylAK2jApZF0A5aTmJa8NK4pc0ELK9AdlgpVQ6ZKIihDZ1IzXpS3oFF0dfQfvPkcbovpwo-_TSpUzIjgUPHlMUX5kGe9C8LZRg09X-y9FQO0DVseAVQpYHQJWPInoURQSuX-3_s_6H9UPGwp8mQ</recordid><startdate>20200601</startdate><enddate>20200601</enddate><creator>Toan, Nguyen Thi</creator><creator>Thuy, Le Quang</creator><general>Springer Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20200601</creationdate><title>The Lipschitz Properties of the Value Function and the Solution Map to a Parametric Discrete Optimal Control Problem</title><author>Toan, Nguyen Thi ; Thuy, Le Quang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-399944bc330ac4979d60351d585dc466273699078347480ba817b119fd45d8e63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Control stability</topic><topic>Dynamic programming</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Optimal control</topic><topic>Parameter sensitivity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Toan, Nguyen Thi</creatorcontrib><creatorcontrib>Thuy, Le Quang</creatorcontrib><collection>CrossRef</collection><jtitle>Acta mathematica vietnamica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Toan, Nguyen Thi</au><au>Thuy, Le Quang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Lipschitz Properties of the Value Function and the Solution Map to a Parametric Discrete Optimal Control Problem</atitle><jtitle>Acta mathematica vietnamica</jtitle><stitle>Acta Math Vietnam</stitle><date>2020-06-01</date><risdate>2020</risdate><volume>45</volume><issue>2</issue><spage>365</spage><epage>382</epage><pages>365-382</pages><issn>0251-4184</issn><eissn>2315-4144</eissn><abstract>Motivated by the works of Toan and Kien (
J. Nonlinear Convex Anal.
12
:635–650,
2011
) and Thuy and Toan (
Acta Math. Vietnam.
43
:175–199,
2018
) on the stability and the solution sensitivity in parametric discrete optimal control problems, this paper is devoted to the study of the Lipschitz property of the value function and the Aubin property of the solution map to a parametric dynamic programming problem with linear constraints. By establishing abstract results on the Lipschitz property of the value function to a parametric programming and the Aubin property of the solution map to a parametric variational inequality, we obtain the Lipschitz property of the value function and the Aubin property of the solution map to a parametric discrete optimal control problem.</abstract><cop>Singapore</cop><pub>Springer Singapore</pub><doi>10.1007/s40306-020-00371-5</doi><tpages>18</tpages></addata></record> |
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| ispartof | Acta mathematica vietnamica, 2020-06, Vol.45 (2), p.365-382 |
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| language | eng |
| recordid | cdi_proquest_journals_2417506527 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Control stability Dynamic programming Mathematics Mathematics and Statistics Optimal control Parameter sensitivity |
| title | The Lipschitz Properties of the Value Function and the Solution Map to a Parametric Discrete Optimal Control Problem |
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