Family of Projected Descent Methods for Optimization Problems with Simple Bounds

Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent direc...
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Gespeichert in:

Autor*in:	Schwartz, A. [verfasserIn] Polak, E.

Format:	Artikel
Sprache:	Englisch

Erschienen:	1997

Systematik:	SA 6420 SA 6420

Anmerkung:	© Plenum Publishing Corporation 1997

Übergeordnetes Werk:	Enthalten in: Journal of optimization theory and applications - Kluwer Academic Publishers-Plenum Publishers, 1967, 92(1997), 1 vom: Jan., Seite 1-31
Übergeordnetes Werk:	volume:92 ; year:1997 ; number:1 ; month:01 ; pages:1-31

Links:	Volltext

DOI / URN:	10.1023/A:1022690711754

Katalog-ID:	OLC2026468702

Internformat


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allfields	10.1023/A:1022690711754 doi (DE-627)OLC2026468702 (DE-He213)A:1022690711754-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Schwartz, A. verfasserin aut Family of Projected Descent Methods for Optimization Problems with Simple Bounds 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems. Polak, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 92(1997), 1 vom: Jan., Seite 1-31 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:92 year:1997 number:1 month:01 pages:1-31 https://doi.org/10.1023/A:1022690711754 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 92 1997 1 01 1-31
spelling	10.1023/A:1022690711754 doi (DE-627)OLC2026468702 (DE-He213)A:1022690711754-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Schwartz, A. verfasserin aut Family of Projected Descent Methods for Optimization Problems with Simple Bounds 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems. Polak, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 92(1997), 1 vom: Jan., Seite 1-31 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:92 year:1997 number:1 month:01 pages:1-31 https://doi.org/10.1023/A:1022690711754 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 92 1997 1 01 1-31
allfields_unstemmed	10.1023/A:1022690711754 doi (DE-627)OLC2026468702 (DE-He213)A:1022690711754-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Schwartz, A. verfasserin aut Family of Projected Descent Methods for Optimization Problems with Simple Bounds 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems. Polak, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 92(1997), 1 vom: Jan., Seite 1-31 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:92 year:1997 number:1 month:01 pages:1-31 https://doi.org/10.1023/A:1022690711754 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 92 1997 1 01 1-31
allfieldsGer	10.1023/A:1022690711754 doi (DE-627)OLC2026468702 (DE-He213)A:1022690711754-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Schwartz, A. verfasserin aut Family of Projected Descent Methods for Optimization Problems with Simple Bounds 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems. Polak, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 92(1997), 1 vom: Jan., Seite 1-31 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:92 year:1997 number:1 month:01 pages:1-31 https://doi.org/10.1023/A:1022690711754 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 92 1997 1 01 1-31
allfieldsSound	10.1023/A:1022690711754 doi (DE-627)OLC2026468702 (DE-He213)A:1022690711754-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Schwartz, A. verfasserin aut Family of Projected Descent Methods for Optimization Problems with Simple Bounds 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems. Polak, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 92(1997), 1 vom: Jan., Seite 1-31 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:92 year:1997 number:1 month:01 pages:1-31 https://doi.org/10.1023/A:1022690711754 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 92 1997 1 01 1-31
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title_full	Family of Projected Descent Methods for Optimization Problems with Simple Bounds
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title_sort	family of projected descent methods for optimization problems with simple bounds
title_auth	Family of Projected Descent Methods for Optimization Problems with Simple Bounds
abstract	Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems. © Plenum Publishing Corporation 1997
abstractGer	Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems. © Plenum Publishing Corporation 1997
abstract_unstemmed	Abstract This paper presents a family of projected descent direction algorithms with inexact line search for solving large-scale minimization problems subject to simple bounds on the decision variables. The global convergence of algorithms in this family is ensured by conditions on the descent directions and line search. Whenever a sequence constructed by an algorithm in this family enters a sufficiently small neighborhood of a local minimizer ○ satisfying standard second-order sufficiency conditions, it gets trapped and converges to this local minimizer. Furthermore, in this case, the active constraint set at ○ is identified in a finite number of iterations. This fact is used to ensure that the rate of convergence to a local minimizer, satisfying standard second-order sufficiency conditions, depends only on the behavior of the algorithm in the unconstrained subspace. As a particular example, we present projected versions of the modified Polak–Ribière conjugate gradient method and the limited-memory BFGS quasi-Newton method that retain the convergence properties associated with those algorithms applied to unconstrained problems. © Plenum Publishing Corporation 1997
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title_short	Family of Projected Descent Methods for Optimization Problems with Simple Bounds
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