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Optimality results for a specific fractional problem
| 1. | LAMA, FSDM, Sidi Mohamed Ben Abdellah University, Fez, Morocco |
In this paper, one minimizes a fractional function over a compact set. Using an exact separation theorem, one gives necessary optimality conditions for strict optimal solutions in terms of Fréchet subdifferentials. All data are assumed locally Lipschitz.
References:
| [1] |
A. Y. Kruger,
On Fréchet subdifferentials, Journal of Mathematical Sciences, 116 (2003), 3325-3358.
doi: 10.1023/A:1023673105317. |
| [2] |
B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Grundlehren Series (Fundamental Principles of Mathematical Sciences) 330, Springer, Berlin, 2006. |
| [3] |
B. S. Mordukhovich and Y. Shao,
Nonsmooth sequential analysis in Asplund spaces, Transactions of the American Mathematical Society, 348 (1996), 1235-1280.
doi: 10.1090/S0002-9947-96-01543-7. |
| [4] |
B. S. Mordukhovich, N. M. Nam and N. D. Yen,
Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming, Optimization, 55 (2006), 685-708.
doi: 10.1080/02331930600816395. |
| [5] |
R. R. Phelps, Convex Functions, Monotone Operators and Differentiability, Springer-Verlag, Berlin, 1993. |
| [6] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processe, Wiley, New York, 1962. |
| [7] |
R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-642-02431-3. |
| [8] |
X. Y. Zheng, Z. Yang and J. Zou,
Exact separation theorem for closed sets in Asplund spaces, Optimization, 66 (2017), 1065-1077.
doi: 10.1080/02331934.2017.1316503. |
show all references
References:
| [1] |
A. Y. Kruger,
On Fréchet subdifferentials, Journal of Mathematical Sciences, 116 (2003), 3325-3358.
doi: 10.1023/A:1023673105317. |
| [2] |
B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Grundlehren Series (Fundamental Principles of Mathematical Sciences) 330, Springer, Berlin, 2006. |
| [3] |
B. S. Mordukhovich and Y. Shao,
Nonsmooth sequential analysis in Asplund spaces, Transactions of the American Mathematical Society, 348 (1996), 1235-1280.
doi: 10.1090/S0002-9947-96-01543-7. |
| [4] |
B. S. Mordukhovich, N. M. Nam and N. D. Yen,
Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming, Optimization, 55 (2006), 685-708.
doi: 10.1080/02331930600816395. |
| [5] |
R. R. Phelps, Convex Functions, Monotone Operators and Differentiability, Springer-Verlag, Berlin, 1993. |
| [6] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processe, Wiley, New York, 1962. |
| [7] |
R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-642-02431-3. |
| [8] |
X. Y. Zheng, Z. Yang and J. Zou,
Exact separation theorem for closed sets in Asplund spaces, Optimization, 66 (2017), 1065-1077.
doi: 10.1080/02331934.2017.1316503. |
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