WEAK SECOND-ORDER OPTIMALITY CONDITIONS
Abstract
The aim of the present article is to derive so-called weak second-order necessary optimality conditions for nonlinear programming problems. Necessary weak second-order optimality conditions are proved under some additional requirements to the constraints.
About the Author
A. E. Leschov
Belarusian State University of Informatics and Radioelectronics
Belarus
Belarus
References
1. Габасов Р. Ф., Кириллова Ф. М. Методы оптимизации. Минск, 1981.
2. Гороховик В. В. Конечномерные задачи оптимизации. Минск, 2007.
3. Ioffe A. D. // SIAM J. Control Optimiz. 1979. Vol. 17. P. 266-288.
4. Bonnans J. F., Shapiro A. Perturbation Analysis of Optimization Problems. New York, 2000.
5. Luderer B., Minchenko L., Satsura T. Multivalued analysis and nonlinear programming problems with perturbations. Dordrecht. 2002
6. FiaccoA. V., McCormick G. P. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. New York, 1968.
7. Bertsekas D. P. Nonlinear Programming. Massachusetts, 1999.
8. Guo L., Lin G. H, Ye J. J. // J. Optimiz. Theory. Appl. 2013. Vol. 158. P. 33-64.
9. FletcherR. Practical Methods of Optimization. London, 1987.
10. Nocedal J., Wright S. J. Numerical Optimization. New York, 1999.
11. Baccari A., Trad A. // SIAM J. Optimization. 2004. Vol. 15. P. 394-408.
12. Andreani R., Echague C. E., SchuverdtM. L. // J. Optim. Theory Appl. 2010. Vol. 146. P. 255-266.
13. MinchenkoL., StakhovskiS. // SIAM J. Optimiz. 2011. Vol. 21. P. 314-332.
14. McCormick G. P. // SIAM J. Appl. Math. 1967. Vol. 15. P. 641-652.
15. Gould N. I. M., TointP. L. // Math. Program. 1999. Vol. 85. P. 433-438.
16. Andreani R., Martinez J. M., Schuverdt M. L. // Optimization. 2007. Vol. 56. P. 529-542.
17. HuX. M., Ralph D. // J. Optim. Theory and Appl. 2004. Vol. 123. P. 365-390.
18. Izmailov A. F., Solodov M. V // SIAM J. Optim. 2008. Vol. 19. P. 1003-1027.
19. Минченко Л. И., Лещев А. Е. // Докл. НАН Беларуси. 2013. Т. 57, № 6. С. 28-34.
Review
Views: 663
Email this article 