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SENSITIVITY ANALYSIS OF THE VALUE FUNCTION FOR PARAMETRIC MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS.

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Title: SENSITIVITY ANALYSIS OF THE VALUE FUNCTION FOR PARAMETRIC MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS.
Authors: LEI GUO1,2,3 guolayne@gmail.com, GUI-HUA LIN4 guihualin@shu.edu.cn, YE, JANE J.2 janeye@uvic.ca, JIN ZHANG2 zhangjin@uvic.ca
Source: SIAM Journal on Optimization. 2014, Vol. 24 Issue 3, p1206-1237. 32p.
Subjects: Mathematical programming, Sensitivity analysis, Directional derivatives, Subdifferentials, Constraint algorithms
Abstract: In this paper, we perform sensitivity analysis of the value function for parametric mathematical programs with equilibrium constraints (MPEC). We show that the value function is directionally differentiable in every direction under the MPEC relaxed constant rank regularity condition, the MPEC no nonzero abnormal multiplier constraint qualification, and the restricted inf-compactness condition. This result is new even in the setting of nonlinear programs in which case it means that under the relaxed constant rank regularity condition, the Mangasarian-Fromovitz constraint qualification, and the restricted inf-compactness condition, the value function for parametric nonlinear programs is directionally differentiable in every direction. Enhanced Mordukhovich (M-) and Clarke (C-) stationarity conditions are M- and C-stationarity conditions with certain enhanced properties and the sets of enhanced M- and C-multipliers axe usually smaller than their associated sets of M- and C-multipliers. In this paper, we give upper estimates for the subdifferential of the value function in terms of the enhanced M- and C-multipliers, respectively. Such estimates give sharper results than their M- and C-counterparts. [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.)
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  Data: SENSITIVITY ANALYSIS OF THE VALUE FUNCTION FOR PARAMETRIC MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS.
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  Data: <searchLink fieldCode="AR" term="%22LEI+GUO%22">LEI GUO</searchLink><relatesTo>1,2,3</relatesTo><i> guolayne@gmail.com</i><br /><searchLink fieldCode="AR" term="%22GUI-HUA+LIN%22">GUI-HUA LIN</searchLink><relatesTo>4</relatesTo><i> guihualin@shu.edu.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><br /><searchLink fieldCode="AR" term="%22JIN+ZHANG%22">JIN ZHANG</searchLink><relatesTo>2</relatesTo><i> zhangjin@uvic.ca</i>
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  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Optimization%22">SIAM Journal on Optimization</searchLink>. 2014, Vol. 24 Issue 3, p1206-1237. 32p.
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br /><searchLink fieldCode="DE" term="%22Sensitivity+analysis%22">Sensitivity analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Directional+derivatives%22">Directional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Subdifferentials%22">Subdifferentials</searchLink><br /><searchLink fieldCode="DE" term="%22Constraint+algorithms%22">Constraint algorithms</searchLink>
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  Label: Abstract
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  Data: In this paper, we perform sensitivity analysis of the value function for parametric mathematical programs with equilibrium constraints (MPEC). We show that the value function is directionally differentiable in every direction under the MPEC relaxed constant rank regularity condition, the MPEC no nonzero abnormal multiplier constraint qualification, and the restricted inf-compactness condition. This result is new even in the setting of nonlinear programs in which case it means that under the relaxed constant rank regularity condition, the Mangasarian-Fromovitz constraint qualification, and the restricted inf-compactness condition, the value function for parametric nonlinear programs is directionally differentiable in every direction. Enhanced Mordukhovich (M-) and Clarke (C-) stationarity conditions are M- and C-stationarity conditions with certain enhanced properties and the sets of enhanced M- and C-multipliers axe usually smaller than their associated sets of M- and C-multipliers. In this paper, we give upper estimates for the subdifferential of the value function in terms of the enhanced M- and C-multipliers, respectively. Such estimates give sharper results than their M- and C-counterparts. [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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        Value: 10.1137/130929783
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      – Code: eng
        Text: English
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        PageCount: 32
        StartPage: 1206
    Subjects:
      – SubjectFull: Mathematical programming
        Type: general
      – SubjectFull: Sensitivity analysis
        Type: general
      – SubjectFull: Directional derivatives
        Type: general
      – SubjectFull: Subdifferentials
        Type: general
      – SubjectFull: Constraint algorithms
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      – TitleFull: SENSITIVITY ANALYSIS OF THE VALUE FUNCTION FOR PARAMETRIC MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS.
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            NameFull: GUI-HUA LIN
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            NameFull: YE, JANE J.
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              Text: 2014
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