Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces
Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporat...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lee, Sung J. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1989 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag New York Inc 1989 |
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| Übergeordnetes Werk: |
Enthalten in: Applied mathematics & optimization - Springer-Verlag, 1974, 19(1989), 1 vom: Jan., Seite 225-242 |
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| Übergeordnetes Werk: |
volume:19 ; year:1989 ; number:1 ; month:01 ; pages:225-242 |
| Links: |
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| DOI / URN: |
10.1007/BF01448200 |
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| Katalog-ID: |
OLC2072635535 |
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| 245 | 1 | 0 | |a Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces |
| 264 | 1 | |c 1989 | |
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| 500 | |a © Springer-Verlag New York Inc 1989 | ||
| 520 | |a Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. | ||
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| 700 | 1 | |a Nashed, M. Zuhair |4 aut | |
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10.1007/BF01448200 doi (DE-627)OLC2072635535 (DE-He213)BF01448200-p DE-627 ger DE-627 rakwb eng 510 VZ Lee, Sung J. verfasserin aut Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc 1989 Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. Hilbert Space Ordinary Differential Equation Control Problem Minimization Problem Optimal Control Problem Nashed, M. Zuhair aut Enthalten in Applied mathematics & optimization Springer-Verlag, 1974 19(1989), 1 vom: Jan., Seite 225-242 (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:19 year:1989 number:1 month:01 pages:225-242 https://doi.org/10.1007/BF01448200 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_60 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 19 1989 1 01 225-242 |
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10.1007/BF01448200 doi (DE-627)OLC2072635535 (DE-He213)BF01448200-p DE-627 ger DE-627 rakwb eng 510 VZ Lee, Sung J. verfasserin aut Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc 1989 Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. Hilbert Space Ordinary Differential Equation Control Problem Minimization Problem Optimal Control Problem Nashed, M. Zuhair aut Enthalten in Applied mathematics & optimization Springer-Verlag, 1974 19(1989), 1 vom: Jan., Seite 225-242 (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:19 year:1989 number:1 month:01 pages:225-242 https://doi.org/10.1007/BF01448200 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_60 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 19 1989 1 01 225-242 |
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10.1007/BF01448200 doi (DE-627)OLC2072635535 (DE-He213)BF01448200-p DE-627 ger DE-627 rakwb eng 510 VZ Lee, Sung J. verfasserin aut Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc 1989 Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. Hilbert Space Ordinary Differential Equation Control Problem Minimization Problem Optimal Control Problem Nashed, M. Zuhair aut Enthalten in Applied mathematics & optimization Springer-Verlag, 1974 19(1989), 1 vom: Jan., Seite 225-242 (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:19 year:1989 number:1 month:01 pages:225-242 https://doi.org/10.1007/BF01448200 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_60 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 19 1989 1 01 225-242 |
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10.1007/BF01448200 doi (DE-627)OLC2072635535 (DE-He213)BF01448200-p DE-627 ger DE-627 rakwb eng 510 VZ Lee, Sung J. verfasserin aut Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc 1989 Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. Hilbert Space Ordinary Differential Equation Control Problem Minimization Problem Optimal Control Problem Nashed, M. Zuhair aut Enthalten in Applied mathematics & optimization Springer-Verlag, 1974 19(1989), 1 vom: Jan., Seite 225-242 (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:19 year:1989 number:1 month:01 pages:225-242 https://doi.org/10.1007/BF01448200 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_60 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 19 1989 1 01 225-242 |
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10.1007/BF01448200 doi (DE-627)OLC2072635535 (DE-He213)BF01448200-p DE-627 ger DE-627 rakwb eng 510 VZ Lee, Sung J. verfasserin aut Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc 1989 Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. Hilbert Space Ordinary Differential Equation Control Problem Minimization Problem Optimal Control Problem Nashed, M. Zuhair aut Enthalten in Applied mathematics & optimization Springer-Verlag, 1974 19(1989), 1 vom: Jan., Seite 225-242 (DE-627)129095184 (DE-600)7418-4 (DE-576)014431300 0095-4616 nnns volume:19 year:1989 number:1 month:01 pages:225-242 https://doi.org/10.1007/BF01448200 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_60 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 19 1989 1 01 225-242 |
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Enthalten in Applied mathematics & optimization 19(1989), 1 vom: Jan., Seite 225-242 volume:19 year:1989 number:1 month:01 pages:225-242 |
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constrained least-squares solutions of linear inclusions and singular control problems in hilbert spaces |
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Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces |
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Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. © Springer-Verlag New York Inc 1989 |
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Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. © Springer-Verlag New York Inc 1989 |
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Abstract LetH1 andH2 be Hilbert spaces and letN be an algebraic subspace ofH1. The least-squares problem for a linear relationL⊂H1⊕H2 restricted to an algebraic cosetS:=g+N, g ∈ H1, is considered. Various characterizations of a minimizer are derived in the form of inclusion relations that incorporate the constraints, and conditions under which a minimizer exists are developed. In particular, it is shown that generalized forms of the “normal equations” for constrained least-squares problems become “normal inclusions” that involve a multivalued adjoint. The setting includes large classes of constrained least-squares minimization problems and optimal control problems subject to generalized boundary conditions. An application of the abstract theory is given to a singular control problem involving ordinary differential equations with generalized boundary conditions, where the control may generate multiresponses. Characterizations of an optimal solution are developed in the form of inclusions that involve either an integrodifferential equation or a differential equation, and adjoint subspaces and/or solutions of certain linear equations. © Springer-Verlag New York Inc 1989 |
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