First-Order Algorithms for Generalized Semi-Infinite Min-Max Problems

Computational Optimization and Applications

Volumn 13, Issue 1-3, 1999, Pages 137-161

  Polak, Elijah ^a   Qi, Liqun ^b   Sun, Defeng ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Consistent approximations; First order methods; Generalized min max problems; Linear convergence; Optimality functions

Indexed keywords

EID: 0004275347     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008660924636     Document Type: Article

References (19)

1. D. P. Bertsekas, "Nondifferentiable optimization via approximation," Mathematical Programming Study, vol. 3, pp. 1-25, 1975.
2. V. F. Dem'yanov, "Quasidifferentiable functions: necessary conditions and descent directions", Mathematical Programming Study, vol. 29, pp. 20-43, 1986.
3. V. F. Dem'yanov, S. Gamidov, and I. T. Sivelina, "An algorithm for minimizing a certain class of quasidifferentiable functions", Mathematical Programming Study, vol. 29, pp. 74-84, 1986.
4. V. F. Dem'yanov and A. M. Rubinov, Quasidifferential Calculus, Optimization Software Inc.: New York, 1986.
5. G. Di Pillo, L. Grippo, and S. Lucidi, "A smooth transformation of the generalized minimax problem", Journal of Optimization Theory and Applications vol. 95, pp. 1-24, 1997.
6. M. Fukushima, "A descent algorithm for nonsmooth convex optimization," Mathematical Programming, vol. 30, pp. 163-175, 1984.
7. K. C. Kiwiel, "A quadratic approximation method for minimizing a class of quasidifferentiable functions," Numerische Mathematik, vol. 45, 411-430, 1984.
8. K.C. Kiwiel, "A linearization method for minimizing certain quasidifferentiable functions," Mathematical Programming Study, vol. 29, pp. 85-94, 1986.
9. K. C. Kiwiel, "Randomized search directions in descent methods for minimizing certain quasidifferentiable functions," Optimization, vol. 17, pp. 475-485, 1986.
10. K. C. Kiwiel, "Descent methods for quasidifferentiable minimization," Applied Mathematics and Optimization, vol. 18, pp. 163-180, 1988.
11. L. Kuntz and A. Pielczyk, "The method of common descent for a certain class of quasidifferentiable functions," Optimization, vol. 22, pp. 669-679, 1991.
12. G. Papavassilopoulos, "Algorithms for a class of nondifferentiable problems," Journal of Optimization Theory and Applications, vol. 34 pp. 41-82, 1981.
13. O. Pironneau and E. Polak, "On the rate of convergence of certain methods of centers," Mathematical Programming, vol. 2, pp. 230-258, 1972.
14. E. Polak, "Basics of minimax algorithms," in Nonsmooth Optimization and Related Topics, Plenum Press: New York, pp. 343-367, 1989.
15. E. Polak and L. He, "Rate-preserving discretization strategies for semi-infinite programming and optimal control," SIAM Journal on Control and Optimization, vol. 30, pp. 548-572, 1992.
16. E. Polak, "On the use of consistent approximations in the solution of semi-infinite optimization and optimal control problems," Mathematical Programming, vol. 62, pp. 385-414, 1993.
17. E. Polak, Optimization: Algorithms and Consistent Approximations, Springer: New York, 1997.
18. L.N. Polyakova, "On the minimization of a quasidifferentiable function subject to equality-type quasidifferentiable constraints, " Mathematical Programming Study, vol. 29, pp. 44-55, 1986.
19. B. N. Pshenichnyi and Yu. M. Danilin, Numerical Methods in Extremal Problems, Chislennye Metody v Ekstremal'nykh Zadachakh, Nauka, Moscow, 1975.