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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]
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Database: Engineering Source
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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]
ISSN:10526234
DOI:10.1137/130929783