Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints
We present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. This is a technical condition that is always satisfied in the case of semi-definite optimization . We derive Lipschitz and Hölder expansions o...
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| Veröffentlicht in: | Mathematics of operations research 1998-11, Vol.23 (4), p.806-831 |
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| container_title | Mathematics of operations research |
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| creator | Bonnans, J. Frederic Cominetti, Roberto Shapiro, Alexander |
| description | We present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. This is a technical condition that is always satisfied in the case of semi-definite optimization . We derive Lipschitz and Hölder expansions of approximate optimal solutions, under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem. We show how the theory applies to semi-infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds, and discuss the differentiability of metric projections as well as the Moreau-Yosida regularization. Finally we show how the theory applies to semi-definite optimization. |
| doi_str_mv | 10.1287/moor.23.4.806 |
| format | Article |
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Frederic</creatorcontrib><creatorcontrib>Cominetti, Roberto</creatorcontrib><creatorcontrib>Shapiro, Alexander</creatorcontrib><title>Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints</title><title>Mathematics of operations research</title><description>We present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. This is a technical condition that is always satisfied in the case of semi-definite optimization . We derive Lipschitz and Hölder expansions of approximate optimal solutions, under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem. We show how the theory applies to semi-infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds, and discuss the differentiability of metric projections as well as the Moreau-Yosida regularization. Finally we show how the theory applies to semi-definite optimization.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Approximation</subject><subject>Banach space</subject><subject>directional constraint qualification</subject><subject>directional differentiability</subject><subject>Exact sciences and technology</subject><subject>Lagrange multipliers</subject><subject>Mathematical functions</subject><subject>Mathematical inequalities</subject><subject>Mathematical programming</subject><subject>metric projection</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Operations research</subject><subject>Optimal solutions</subject><subject>optimal value function</subject><subject>Optimization</subject><subject>Optimization. Search problems</subject><subject>parametric optimization</subject><subject>second order optimality conditions</subject><subject>semi-definite programming</subject><subject>semi-infinite programming</subject><subject>Sensitivity analysis</subject><subject>Studies</subject><subject>Sufficient conditions</subject><subject>Tangents</subject><subject>Trajectories</subject><issn>0364-765X</issn><issn>1526-5471</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><recordid>eNqFkEtrGzEUhUVoIW7aZXddDKWQTcbVW-NlMM0DAg55QHdCkaVYZkZydeUG99dHZhKaXRZCiPOdc68OQl8JnhLaqZ9DSnlK2ZRPOywP0IQIKlvBFfmAJphJ3iopfh-iTwBrjIlQhE_Q3a2LEEr4G8quOY2m30GAJvlmsSlhCP9MCSk21zk99G6A5j4uXW5unU1x2Szy_nHjHre9yc08RSjZhFjgM_roTQ_uy8t9hO7Pft3NL9qrxfnl_PSqtbyTpe0knTErvKl7cio7xZ1kRjwIybsOz4j1XglpjRQcU-ol597SehjHsuNqyY7Q9zF3k9OfrYOi12mb6ydAU0Kl4gzjCrUjZHMCyM7rTQ6DyTtNsN73pve9aco017W3yv94CTVgTe-ziTbAf5OquxJVsW8jtoZS7a8yk7Oawap8Msoh-pQHeHfo8YivwuPqKWSnX32DKau35DPwHJOs</recordid><startdate>19981101</startdate><enddate>19981101</enddate><creator>Bonnans, J. Frederic</creator><creator>Cominetti, Roberto</creator><creator>Shapiro, Alexander</creator><general>INFORMS</general><general>Institute for Operations Research and the Management Sciences</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>19981101</creationdate><title>Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints</title><author>Bonnans, J. Frederic ; Cominetti, Roberto ; Shapiro, Alexander</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c486t-86293c5fa526426874e63a5b56488091cff756ca654022f644fc24fc3406847d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Approximation</topic><topic>Banach space</topic><topic>directional constraint qualification</topic><topic>directional differentiability</topic><topic>Exact sciences and technology</topic><topic>Lagrange multipliers</topic><topic>Mathematical functions</topic><topic>Mathematical inequalities</topic><topic>Mathematical programming</topic><topic>metric projection</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Operations research</topic><topic>Optimal solutions</topic><topic>optimal value function</topic><topic>Optimization</topic><topic>Optimization. Search problems</topic><topic>parametric optimization</topic><topic>second order optimality conditions</topic><topic>semi-definite programming</topic><topic>semi-infinite programming</topic><topic>Sensitivity analysis</topic><topic>Studies</topic><topic>Sufficient conditions</topic><topic>Tangents</topic><topic>Trajectories</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bonnans, J. Frederic</creatorcontrib><creatorcontrib>Cominetti, Roberto</creatorcontrib><creatorcontrib>Shapiro, Alexander</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Mathematics of operations research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bonnans, J. Frederic</au><au>Cominetti, Roberto</au><au>Shapiro, Alexander</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints</atitle><jtitle>Mathematics of operations research</jtitle><date>1998-11-01</date><risdate>1998</risdate><volume>23</volume><issue>4</issue><spage>806</spage><epage>831</epage><pages>806-831</pages><issn>0364-765X</issn><eissn>1526-5471</eissn><coden>MOREDQ</coden><abstract>We present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. This is a technical condition that is always satisfied in the case of semi-definite optimization . We derive Lipschitz and Hölder expansions of approximate optimal solutions, under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem. We show how the theory applies to semi-infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds, and discuss the differentiability of metric projections as well as the Moreau-Yosida regularization. Finally we show how the theory applies to semi-definite optimization.</abstract><cop>Linthicum, MD</cop><pub>INFORMS</pub><doi>10.1287/moor.23.4.806</doi><tpages>26</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Mathematics of operations research, 1998-11, Vol.23 (4), p.806-831 |
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| language | eng |
| recordid | cdi_pascalfrancis_primary_1764217 |
| source | INFORMS PubsOnLine; JSTOR Mathematics & Statistics; EBSCOhost Business Source Complete; JSTOR Archive Collection A-Z Listing |
| subjects | Algorithms Applied sciences Approximation Banach space directional constraint qualification directional differentiability Exact sciences and technology Lagrange multipliers Mathematical functions Mathematical inequalities Mathematical programming metric projection Operational research and scientific management Operational research. Management science Operations research Optimal solutions optimal value function Optimization Optimization. Search problems parametric optimization second order optimality conditions semi-definite programming semi-infinite programming Sensitivity analysis Studies Sufficient conditions Tangents Trajectories |
| title | Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints |
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