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STABILITY ANALYSIS FOR PARAMETRIC MATHEMATICAL PROGRAMS WITH GEOMETRIC CONSTRAINTS AND ITS APPLICATIONS.

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Title: STABILITY ANALYSIS FOR PARAMETRIC MATHEMATICAL PROGRAMS WITH GEOMETRIC CONSTRAINTS AND ITS APPLICATIONS.
Authors: LEI GUO1 lei_guo_opt@yahoo.com.cn, GUI-HUA LIN1 lin_g_h@yahoo.com.cn, YE, JANE J.2 janeye@uvic.ca
Source: SIAM Journal on Optimization. 2012, Vol. 22 Issue 3, p1151-1176. 26p.
Subjects: Mathematical programming, Mathematical mappings, Continuous functions, Variational approach (Mathematics), Perturbation theory
Abstract: This paper studies stability for parametric mathematical programs with geometric constraints. We show that, under the no nonzero abnormal multiplier constraint qualification and the second-order growth condition or second-order sufficient condition, the locally optimal solution mapping and stationary point mapping are nonempty-valued and continuous with respect to the perturbation parameter and, under some suitable conditions, the stationary pair mapping is calm. Furthermore, we apply the above results to parametric mathematical programs with equilibrium constraints. In particular, we show that the M-stationary pair mapping is calm with respect to the perturbation parameter if the M-multiplier second-order sufficient condition is satisfied, and the S-stationary pair mapping is calm if the S-multiplier second-order sufficient condition is satisfied and the bidegenerate index set is empty. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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PubType: Academic Journal
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  Data: STABILITY ANALYSIS FOR PARAMETRIC MATHEMATICAL PROGRAMS WITH GEOMETRIC CONSTRAINTS AND ITS APPLICATIONS.
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  Data: <searchLink fieldCode="AR" term="%22LEI+GUO%22">LEI GUO</searchLink><relatesTo>1</relatesTo><i> lei_guo_opt@yahoo.com.cn</i><br /><searchLink fieldCode="AR" term="%22GUI-HUA+LIN%22">GUI-HUA LIN</searchLink><relatesTo>1</relatesTo><i> lin_g_h@yahoo.com.cn</i><br /><searchLink fieldCode="AR" term="%22YE%2C+JANE+J%2E%22">YE, JANE J.</searchLink><relatesTo>2</relatesTo><i> janeye@uvic.ca</i>
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  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Optimization%22">SIAM Journal on Optimization</searchLink>. 2012, Vol. 22 Issue 3, p1151-1176. 26p.
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+mappings%22">Mathematical mappings</searchLink><br /><searchLink fieldCode="DE" term="%22Continuous+functions%22">Continuous functions</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+approach+%28Mathematics%29%22">Variational approach (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink>
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  Data: This paper studies stability for parametric mathematical programs with geometric constraints. We show that, under the no nonzero abnormal multiplier constraint qualification and the second-order growth condition or second-order sufficient condition, the locally optimal solution mapping and stationary point mapping are nonempty-valued and continuous with respect to the perturbation parameter and, under some suitable conditions, the stationary pair mapping is calm. Furthermore, we apply the above results to parametric mathematical programs with equilibrium constraints. In particular, we show that the M-stationary pair mapping is calm with respect to the perturbation parameter if the M-multiplier second-order sufficient condition is satisfied, and the S-stationary pair mapping is calm if the S-multiplier second-order sufficient condition is satisfied and the bidegenerate index set is empty. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of SIAM Journal on Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Mathematical mappings
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      – SubjectFull: Continuous functions
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      – SubjectFull: Variational approach (Mathematics)
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      – TitleFull: STABILITY ANALYSIS FOR PARAMETRIC MATHEMATICAL PROGRAMS WITH GEOMETRIC CONSTRAINTS AND ITS APPLICATIONS.
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              Text: 2012
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