Dual parameterization approach to linear-quadratic semi-infinite programming problems

Optimization Methods and Software

Volumn 10, Issue 3, 1999, Pages 471-495

  Liu, Y ^a   Teo, K L ^a   Ito, S ^b  

^a CURTIN UNIVERSITY   (Australia)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; DECISION THEORY; LINEAR PROGRAMMING; PROBLEM SOLVING;

DUALITY THEORY; LINEAR QUADRATIC SEMI-INFINITE PROGRAMMING;

QUADRATIC PROGRAMMING;

EID: 0032627674     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556789908805725     Document Type: Article

References (20)

1. Blankenship, J. W. and Falk, J. E. (1976). Infinitely constrained optimization problems, J. Optim. Theory Appl., 19(2), 261-281.
2. Cesari, L. (1983). Optimization Theory and Applications, Springer-Verlag, New York,
3. Fletcher, R. (1987). Practical Methods of Optimization, Second Edition, John Wiley, Chichester.
4. Grace, A. (1990). OPTIMIZATION TOOLBOX user's guide, The Math Works, Inc., Nov.
5. Gribik, P. R. (1979). A central cutting plane algorithm for semi-infinite programming problems, in Semi-Infinite Programming, R. Hettich ed., Lecture Notes in Control and Inform. Sci. 15, Springer-Verlag, Berlin, Heidelberg, New York, pp. 66-82.
6. Gribik, P. R. (1979). Selected applications of semi-infinite programming, in Constructive Approaches to Mathematical Models, C. V. Coffman and G. J. Fix, eds., Academic Press, New York, pp. 171-188.
7. Gonzaga, C., Polak, E. and Traham, R. (1980). An improved algorithm for optimization problems with functional inequality constraints, IEEE Trans. Automat. Control, AC-25, 49-54.
8. Gustafson, S.-Å. and Kortanek, K. O. (1973). Numerical treatment of a class of semi-infinite programming problems, Naval Research Logistics Quart., 477-504.
9. Hettich, R. and Kortanek, K. O. (1993). Semi-infinite programming: Theory, method, and applications, SIAM Review, 35, 380-429.
10. Ito, S. and Shimizu, K. (1991). Dual quasi-Newton algorithm for infinitely constrained optimization problems (in Japanese), Trans. Soc. Instrument. Contr. Engineers, 27(4), 452-457.
11. Jennings, L. S. and Teo, K. L. (1990). A computational algorithm for functional inequality constrained optimization problems, Automatica, 26, 371-375.
12. Kolmogorov, A. N. and Fomin, S. V. (1970). Introductory Real Analysis, Prentice-Hall, Englewood Cliffs, NJ.
13. Kortanek, K. O. and Hoon No (1993). A central cutting plane algorithm for convex semi-infinite programming problems, SIAM J. Optim., 3, 901-918.
14. Luenberger, D. G. (1969). Optimization by Vector Space Method, John Wiley and Sons Inc. New York-London-Sydney-Toronto.
15. Eliane R. Panier and André L. Tits (1989). A globally convergent algorithm with adaptively refined discretization for semi-infinite optimization problems arising in engineering design, IEEE Trans. Automat. Control, 34, 903-908.
16. Polak, E. (1987). On the mathematical foundations of non-differential optimization in engineering design, SIAM Review, 29, 21-89.
17. Polak, E., Mayne, D. Q. and Stimler, D. M. (1984). Control system design via semi-infinite optimization: A review, Proc. IEEE, 72, 1777-1794.
18. Teo, K. L., Goh, C. J. and Wong, K. H. (1991). A Unified Computational Approach to Optimal Control Problems, Longman Scientific and Technical, London.
19. Teo, K. L., Rehbock, V. and Jennings, L. S. (1993). A new computational algorithm for functional inequality constrained optimization problems, Automatica, 29(3), 789-792.
20. Zang, Z., Vo, B., Cantoni, A. and Teo, K. L. (1994). Continuous-time envelope constrained filter design via orthonormal filters, Technical report, Australian telecommunications research institute, ID No. SPL-TM007.