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. |
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| 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] |
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| Database: | Engineering Source |
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