A practical algorithm for minimizing a rank-two saddle function on a polytope

Journal of the Operations Research Society of Japan

Volumn 39, Issue 1, 1996, Pages 63-76

  Kuno, Takahito ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002260113     PISSN: 04534514     EISSN: None     Source Type: Journal    
DOI: 10.15807/jorsj.39.63     Document Type: Article

References (26)

1. Adler, I., ''The expected number of pivots needed to solve parametric linear programs and the efficiency of the self-dual simplex method," Draft, Department of IEOR, University of California, Berkeley (CA, 1983).
2. Chvǎtal, V., Linear Programming, Freeman and Company (NY, 1983).
3. Gal, T., "Linear parametric programming - a brief survey," Mathematical Programming Study 21 (1984), 43 - 68.
4. Geoffrion, M., "Solving bicriterion mathematical programs," Operations Research 15 (1967), 39 - 54.
5. Haimovich, M., ''The simplex method is very good! - On the expected number of pivot steps and related properties of random linear programs," Draft, Uris Hall, Columbia University (NY, 1983).
6. [G] Henderson, J. M. and R. E. Quandt, Microeconomic Theory, Mcgraw-Hill (NY, 1971).
7. Horst, R. and H. Tuy, Global Optimization: Deterministic Approaches, Springer-Verlag (Berlin, 1990).
8. Konno, H. and M. Inori, ''Bond portfolio optimization by bilinear fractional programming," Journal of the Operations Research Society of Japan 32 (1988). 143 - 158.
9. Konno, H. and T. Kuno, "Linear multiplicative programming," Mathematical Programming 56 (1992), 51 - 64.
10. Konno, H. and T. Kuno, ''Multiplicative programming problems.'" in R. Horst and P.M. Pardalos (eds.), Handbook of Global Optimization. Kluwer Academic Publishers (Dortrecht, 1995).
11. Konno, H., T. Kuno, S. Suzuki, P. T. Thach and Y. Yajima, "Global optimization techniques for a problem in the plane," Report IHSS91-36, Institute of Human and Social Sciences, Tokyo Institute of Technology (Tokyo, 1991).
12. Konno, H., T. Kuno and Y. Yajima, "Parametric simplex algorithms for a class of NP complete problems whose average number of steps are polynomial." Computational Optimization and Applications 1 (1992), 227 - 239.
13. Konno, H., Y. Yajima and T. Matsui, "Parametric simplex algorithms for solving a special class of noucouvex minimization problems," Journal of Global Optimization 1 (1991), 65 - 82.
14. Kuno, T., "Globally determining a minimum-area rectangle enclosing the projection of a higher-dimensional set," Operations Research Letters 13 (1993). 295 - 303.
15. Kuno, T., and Y. Yamamoto, "A parametric simplex algorithm for solving a class of rank-two reverse convex programs," Report ISE-TR-93-103. Institute of Information Sciences and Electronics, University of Tsukuba (Tsukuba, 1993).
16. Muu, L. D., "An algorithm for solving convex programs with an additional convex-concave constraint," Mathematical Programming 61 (1993), 75 - 87.
17. Muu, L. D. and W. Oettli, "Method for minimizing a convex-concave function over a convex set," Journal of Optimization Theory and Application 70 (1991), 377 - 384.
18. Pardalos, P. M., "Polynomial time algorithms for some classes of constrained nonconvex quadratic problems," Optimization 21 (1990), 843 - 853.
19. Pardalos, P. M. and S. A. Vavasis, "Quadratic programming with one negative eigen-value is NP-hard," Journal of Global Optimization 1 (1991), 15 - 22.
20. Schrijver, A., Theory of Linear and Integer Programming. John-Wiley & Sons (NY, 1986).
21. Shamir, R., "The efficiency of the simplex method: a survey," Management Science 33 (1987), 301 - 334.
22. Sniedovich, M., Macalalag, E. and S. Findlay, "The simplex method as a global optimizer: a c-programming perspective," Journal of Global Optimization 4 (1994), 89 -109.
23. Swamp, K., "Indefinite quadratic programming." Cahiers du Centre d'Études de Recherche Opérationnelle 8 (1966), 217 - 222.
24. Tuy, H., "The complementary convex structure in global optimization," Journal of Global Optimization 2 (1992), 21 - 40.
25. Tuy, H., S. Ghannadan. A. Migdalas and P. Värbrand. "Strongly polynomial algorithm for a production-transportation problem with concave production costs." Optimization 27 (1993), 205 - 227.
26. Vavasis, S. A., ''Quadratic programming is in NP," Information Processing Letters 36 (1990), 73 - 77.