Dual-based methods for solving infinite-horizon nonstationary deterministic dynamic programs
We develop novel dual-ascent and primal-dual methods to solve infinite-horizon nonstationary deterministic dynamic programs. These methods are finitely implementable and converge in value to optimality. Moreover, the dual-ascent method produces a sequence of improving dual solutions that pointwise c...
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| Veröffentlicht in: | Mathematical programming 2021-05, Vol.187 (1-2), p.253-285 |
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| creator | Ryan, Christopher Thomas Smith, Robert L. |
| description | We develop novel dual-ascent and primal-dual methods to solve infinite-horizon nonstationary deterministic dynamic programs. These methods are finitely implementable and converge in value to optimality. Moreover, the dual-ascent method produces a sequence of improving dual solutions that pointwise converge to an optimal dual solution, while the primal-dual algorithm provides a sequence of primal basic feasible solutions with value error bounds from optimality that converge to zero. Our dual-based methods work on a more general class of infinite network flow problems that include the shortest-path formulation of dynamic programs as a special case. To our knowledge, these are the first dual-based methods proposed in the literature to solve infinite-horizon nonstationary deterministic dynamic programs. |
| doi_str_mv | 10.1007/s10107-020-01478-1 |
| format | Article |
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To our knowledge, these are the first dual-based methods proposed in the literature to solve infinite-horizon nonstationary deterministic dynamic programs.</description><subject>Algorithms</subject><subject>Ascent</subject><subject>Basic converters</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Combinatorics</subject><subject>Convergence</subject><subject>Full Length Paper</subject><subject>Horizon</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Numerical Analysis</subject><subject>Optimization</subject><subject>Shortest-path problems</subject><subject>Theoretical</subject><issn>0025-5610</issn><issn>1436-4646</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKt_wNWA6-i9k9d0KfUJghvdCSEzk7RTOklNUqH-eqMV3Lm6m-87h3sIOUe4RAB1lRAQFIUaKCBXDcUDMkHOJOWSy0MyAagFFRLhmJyktAIAZE0zIW83W7OmrUm2r0abl6FPlQuxSmH9MfhFNXg3-CFbugxx-Ay-8sGnbPIQvIm7qrfZxrEQKQ9d1e-8GcvdxLCIZkyn5MiZdbJnv3dKXu9uX-YP9On5_nF-_UQ7hrNMhTGtsw4EA4Fq1irhpO162Rhr684paJycsQY7Lhs0HCQ3KLlAxlStULZsSi72uaX4fWtT1quwjb5U6lqgUMVWdaHqPdXFkFK0Tm_iMJYvNIL-XlHvV9RlRf2zosYisb2UCuwXNv5F_2N9AauUdhs</recordid><startdate>20210501</startdate><enddate>20210501</enddate><creator>Ryan, Christopher Thomas</creator><creator>Smith, Robert L.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-1957-2303</orcidid></search><sort><creationdate>20210501</creationdate><title>Dual-based methods for solving infinite-horizon nonstationary deterministic dynamic programs</title><author>Ryan, Christopher Thomas ; Smith, Robert L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-5aabfef05305179b75f6ecd68aee2cf708f69381c4681a4064a164513372716b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algorithms</topic><topic>Ascent</topic><topic>Basic converters</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Combinatorics</topic><topic>Convergence</topic><topic>Full Length Paper</topic><topic>Horizon</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Numerical Analysis</topic><topic>Optimization</topic><topic>Shortest-path problems</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ryan, Christopher Thomas</creatorcontrib><creatorcontrib>Smith, Robert L.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Mathematical programming</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ryan, Christopher Thomas</au><au>Smith, Robert L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dual-based methods for solving infinite-horizon nonstationary deterministic dynamic programs</atitle><jtitle>Mathematical programming</jtitle><stitle>Math. 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| subjects | Algorithms Ascent Basic converters Calculus of Variations and Optimal Control Optimization Combinatorics Convergence Full Length Paper Horizon Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Shortest-path problems Theoretical |
| title | Dual-based methods for solving infinite-horizon nonstationary deterministic dynamic programs |
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