Combined entropic regularization and path-following method for solving finite convex min-max problems subject to infinitely many linear constraints

Journal of Optimization Theory and Applications

Volumn 101, Issue 1, 1999, Pages 167-190

  Sheu, R L ^a   Wu, S Y ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

Entropic regularization; Interior point methods; Min max problems; Nonsmooth optimization; Path following methods; Semi infinite programming

Indexed keywords

MATHEMATICAL PROGRAMMING;

ENTROPIC REGULARIZATION; INTERIOR-POINT METHOD; LINEAR CONSTRAINTS; MAX FUNCTIONS; MINIMISATION; MINMAX PROBLEM; NONSMOOTH OPTIMIZATION; PATH-FOLLOWING METHOD; REGULARISATION; SEMI INFINITE PROGRAMMING;

FUNCTIONS;

EID: 0033247732     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021727228957     Document Type: Article

References (26)

1. 1. DI PILLO, G., GRIPPO, L., and LUCIDI, S., A Smooth Method for the Finite Minimax Problem, Mathematical Programming, Vol. 60, pp. 187-214, 1993.
2. 2. DEMYANOV, V. F., and MALOZEMOV, V. N., Introduction to Minimax, John Wiley and Sons, New York, New York, 1974.
3. 3. SHOR, N. Z., Minimization Methods for Nondifferentiable Functions, Translated from the Russian by K. C. Kiwiel and A. Ruszczynski, Springer Verlag, Berlin, Germany, 1985.
4. 4. ANDERSON, E. J., and NASH, P., Linear Programming in Infinite-Dimensional Spaces: Theory and Applications, John Wiley and Sons, New York, New York, 1987.
5. 5. FERRIS, M. C., and PHILPOTT, A. B., An Interior-Point Algorithm for Semi-Infinite Linear Programming, Mathematical Programming, Vol. 43, pp. 257-276, 1989.
6. 6. GUSTAFSON, S. A., and KORTANEK, K. O., Numerical Treatment of a Class of Semi-Infinite Programming Problems, Naval Research Logist Quarterly, Vol. 20, pp. 477-504, 1973.
7. 7. HETTICH, R., and KORTANEK, K. O., Semi-Infinite Programming: Theory, Methods, and Applications, SIAM Review, Vol. 35, pp. 380-429, 1993.
8. 8. FANG, S. C., and WU, S. Y., An Inexact Approach to Solving Linear Semi-Infinite Programming Problems, Optimization, Vol. 28, pp. 291-299, 1994.
9. 9. LIN, C. J., YANG, E. K., FANG, S. C., and WU, S. Y., Implementation of an Inexact Approach to Solving Linear Semi-Infinite Programming Problems, Journal of Computational and Applied Mathematics, Vol. 61, pp. 87-103, 1995.
10. 10. SHEU, R. L., and WU, S. Y., A Primal-Dual Approach for Quadratic Semi-Infinite Programming, Proceedings of the International Mathematics Conference, Kaohsiung, Taiwan, 1994; World Scientific Publishing Company, Singapore, pp. 179-188, 1995.
11. 11. SHEU, R. L., WU, S. Y., and FANG, S. C., A Primal-Dual Infeasible-Interior-Point Algorithm for Linear Semi-Infinite Programming, Computers and Mathematics with Applications, Vol. 29, pp. 7-18, 1995.
12. 12. ZANG, I., A Smooth-Out Technique for Minmax Optimization, Mathematical Programming, Vol. 19, pp. 61-77, 1980.
13. 13. POWELL, M. J. D., An Efficient Method for Finding the Minimum of a Function of Several Variables without Calculating Derivatives, Computer Journal, Vol. 7, pp. 155-162, 1964.
14. 14. STEWARD, G. W., A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives, Journal of the Association for Computing Machinery, Vol. 14, pp. 72-83, 1967.
15. 15. BERTSEKAS, D. P., Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, New York, 1982.
16. 16. GIGOLA, C., and GOMEZ, S., A Regularization Method for Solving the Finite Convex Minmax Problem, SIAM Journal on Numerical Analysis, Vol. 27, pp. 1621-1634, 1990.
17. 17. LI, X. S., and FANG, S. C., On the Entropic Regularization Method for Solving Minmax Problems with Applications, Mathematical Methods of Operations Research (ZOR), Vol. 46, pp. 119-130, 1997.
18. 18. POLYAK, R. A., Smooth Optimization Methods for Minmax Problems, SIAM Journal on Control and Optimization, Vol. 26, pp. 1274-1286, 1988.
19. 19. HIRIART-URRUTY, J. B., and LEMARECHAL, C., Convex Analysis and Minimization Algorithms, Springer Verlag, Berlin, Germany, 1993.
20. 20. ROBERTS, A. W., and VARBERG, D. E., Convex Functions, Academic Press, New York, New York, 1973.
21. 21. ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1972.
22. 22. LUENBERGER, D. G., Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969.
23. 23. DEN HERTOG, D., Interior-Point Approach to Linear, Quadratic, and Convex Programming, Kluwer Academic Publishers, Dordrecht, Netherlands, 1994.
24. 24. Roos, C., and VIAL, J. P., A Polynomial Method of Approximate Centers for Linear Programming, Mathematical Programming, Vol. 54, pp. 295-305, 1992.
25. 25. SHEU, R. L., and FANG, S. C., On the Generalized Path-Following Methods for Linear Programming, Optimization, Vol. 30, pp. 235-249, 1994.
26. 26. MONTEIRO, R. D. C., and ADLER, I., Interior Path-Following Primal-Dual Algorithms, Part 1, Mathematical Programming, Vol. 44, pp. 27-41, 1989.