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Guignard Qualifications and Stationary Conditions for Mathematical Programming with Nonsmooth Switching Constraints | ||
Control and Optimization in Applied Mathematics | ||
مقاله 2، دوره 6، شماره 2، مهر 2021، صفحه 23-35 اصل مقاله (391.3 K) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.30473/coam.2021.60747.1176 | ||
نویسندگان | ||
Fatemeh Gorgini Shabankareh؛ Nader Kanzi؛ Javad Izadi* ؛ Kamal Fallahi | ||
Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran | ||
چکیده | ||
In this paper, some constraint qualifications of the Guignard type are defined for optimization problems with continuously differentiable objective functions and locally Lipschitz switching constraints. Then, a new type of stationary condition, named parametric stationary condition, is presented for the problem, and it is shown that all the stationarity conditions in various papers can be deduced from it. This paper can be considered as an extension of a recent article (see Kanzow, et al.) to the nonsmooth case. Finally, the article ends with two important examples. The results of the article are formulated according to Clark subdifferential and using nonsmooth analysis methods. | ||
کلیدواژهها | ||
Constraint qualification؛ Stationary conditions؛ Optimality conditions؛ Switching constraints | ||
مراجع | ||
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[5] Kanzow C., Mehlitz P., Steck D. (2019). “Relaxation schemes for mathematical programs with switching constraints”, Optimization Methods and Software.
[6] Kazemi S., Kanzi N. (2018). “Constraint qualifications and stationary conditions for mathematical programming with non-differentiable vanishing constraints”, Journal of Optimization Theory and Applications, 179(3), 800-819.
[7] Kazemi S., Kanzi N., Ebadian A. (2019). “Estimating the Frechet normal cone in optimization problems with non-smooth vanishing constraints”, Iranian Journal of Science and Technology, Transactions A Science, 43(5), 2299-2306.
[8] Liang Y. C., Ye J. J. (2021). “Optimality conditions and exact penalty for mathematical programs with switching constraints”, Journal of Optimization Theory and Applications, 190, 1-31.
[9] Mehlitz P. (2020). “Stationarity conditions and constraint qualifications for mathematical programs with switching constraints”, Mathematical Programming, 180(1), 149-186.
[10] Mokhtavayi H., Heydari A., Kanzi N. (2020). “First-order optimality conditions for Lipschitz optimization problems with vanishing constraints”, Iranian Journal of Science and Technology, Transactions A Science, 44 (6), 1853-1861.
[11] Shaker A. J., Kanzi N., Farahmand R. S., Reyhani A. P. (2018). “Characterization of properly efficient solutions for convex multi-objective programming with non-differentiable vanishing constraints”, Control and Optimization in Applied Mathematics, 3(2), 49-58.
[12] Shikhman V. (2021). “Topological approach to mathematical programs with switching constraints”, Set-Valued and Variational Analysis. | ||
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