@article{RO_2000__34_4_397_0, author = {Stancu-Minasian, I. M. and Tigan, Stefan}, title = {Continuous time linear-fractional programming. {The} minimum-risk approach}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {397--409}, publisher = {EDP-Sciences}, volume = {34}, number = {4}, year = {2000}, mrnumber = {1815070}, zbl = {1039.90080}, language = {en}, url = {http://archive.numdam.org/item/RO_2000__34_4_397_0/} }
TY - JOUR AU - Stancu-Minasian, I. M. AU - Tigan, Stefan TI - Continuous time linear-fractional programming. The minimum-risk approach JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2000 SP - 397 EP - 409 VL - 34 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/item/RO_2000__34_4_397_0/ LA - en ID - RO_2000__34_4_397_0 ER -
%0 Journal Article %A Stancu-Minasian, I. M. %A Tigan, Stefan %T Continuous time linear-fractional programming. The minimum-risk approach %J RAIRO - Operations Research - Recherche Opérationnelle %D 2000 %P 397-409 %V 34 %N 4 %I EDP-Sciences %U http://archive.numdam.org/item/RO_2000__34_4_397_0/ %G en %F RO_2000__34_4_397_0
Stancu-Minasian, I. M.; Tigan, Stefan. Continuous time linear-fractional programming. The minimum-risk approach. RAIRO - Operations Research - Recherche Opérationnelle, Tome 34 (2000) no. 4, pp. 397-409. http://archive.numdam.org/item/RO_2000__34_4_397_0/
1. On the solution of a class of continuous linear programs. SIAM J. Control Optim. 32 (1994) 1289-1296. | MR | Zbl
and ,2. Generation of feasible descent directions in continuous-time linear programming, Tech. Report SOL 83-18. Department of Operations Research, Stanford University, Stanford, CA (1983).
,3. Bottleneck problems and dynamic programming. Proc. Nat Acad. Sci. 39 (1953) 947-951. | MR | Zbl
,4. Dynamic Programming. Princeton University Press, Princeton, NJ (1957). | MR | Zbl
,5. On stochastic linear programming, I: Distribution problems: A single random variable. Rev. Roumaine Math. Pures Appl. 8 (1963) 683-697. | MR | Zbl
,6. Programme de risque minimal en programmation linaire stochastique. C. R. Acad. Sci. Paris 259 (1964) 981-983. | MR | Zbl
,7. A class of continuous time programming problems. J. Optim. Theory Appl. 24 (1978) 243-263. | MR | Zbl
and ,8. Numerical solutions to continuous linear programming problems. Oper. Res. 17 (1973) 107-117. | MR | Zbl
, ,9. Deterministic equivalents for optimizing and satisfying under chance constraints. Oper. Res. 11 (1963) 18-39. | MR | Zbl
, ,10. On nonlinear fractional programming. Management Sci. 13 (1967) 492-498. | MR | Zbl
,11. A simplex-like algorithm for continuous-time linear optimal control problems, in Optimization Methods for Resource Allocation, edited by R.W. Cottle and J. Krarup. Crane Russak and Co. Inc., New York (1974) 309-322. | MR
,12. Continuous time programming with nonlinear time-delayed constraints. J. Math. Anal. Appl. 46 (1974) 41-61. | MR | Zbl
and ,13. A class of continuous convex programming problems. J. Math. Anal. Appl. 22 (1968) 427-437. | MR | Zbl
and ,14. Representation extended to continuous time, in Optimization Methods for Resource Allocation, edited by R.W. Cottle and J. Krarup, Crane Russak and Co. Inc., New York (1974) 297-307. | MR
,15. On the form of the linear continuous time programming problem and a conjecture by Tyndall. J. Math. Anal. Appl. 111 (1985) 236-242. | MR | Zbl
and ,16. A generalization of basic feasible solutions to continuous time programming, FSU Statistics Report M-598. The Florida State University, Department of Statistics, Tallahassee, Fla., 32306 (1981).
and ,17. Fundamentals of a continuous time simplex method,, Tech. Report SOL 78-26. Department of Opérations Research, Stanford University, Stanford, CA (1978).
,18. An algorithm for a class of continuous linear programs. SIAM J. Control Optim. 31 (1993) 1558-1577. | MR | Zbl
,19. Forms of optimal solutions for separated continuous linear programs. SIAM J. Control Optim. 33 (1995) 1952-1977. | MR | Zbl
,20. A generalised function setting for dynamic optimal control problems, in Optimization Methods for Resource Allocation, edited by R.W. Cottle and J. Krarup. Crane Russak and Co. Inc., New York (1974) 279-296. | MR
,21. Continuous time programming with set-inclusive constraints and objective set. J. Math. Anal. Appl. 91 (1983) 367-375. | MR | Zbl
,22. Continuous time matrix programming. J. Math. Anal. Appl. 173 (1993) 280-291. | MR | Zbl
and ,23. Stochastic Programming with Multiple Objective Functions. Editura Academiei Române, Bucuresti and D. Reidel Publishing Company, Dordrecht, Boston, Lancester (1984). | MR | Zbl
,24. Metode de rezolvare a problemelor de programare fractionara. Editura Academiei Romane, Bucuresti (1992). | MR | Zbl
,25. Fractional Programming. Theory, Methods and Applications. Kluwer Academic Publishers, Dordrecht/Boston/London (1997). | MR | Zbl
,26. The minimum-risk approach to special problems of mathematical programming. The distribution function of the optimal value. Rev. Anal. Numér. Théor. Approx. 13 (1984) 175-187. | MR | Zbl
and ,27. The minimum-risk approach to max-min bilinear programming. An. Stiint. Univ. Al. I. Cuza lasi Sect. I a Mat. 31 (1985) 205-209. | MR | Zbl
and ,28. A stochastic approach to some linear fractional goal programming problems. Kybernetika (Praha) 24 (1988) 139-149. | MR | Zbl
and ,29. On some fractional programming models occuring in minimum-risk problems, in Generalized Convexity and Fractional Programming with Economic Applications, edited by A. Cambini, E. Castagnoli, L. Martein, P. Mazzoleni and S. Schaible, Proceedings of the International Workshop on "Generalized Convexity and Fractional Programming with Economic Applications" held at the University of Pisa, Italy, May 30 - June 1, 1988. Springer Verlag, Lecture Notes in Econom. and Math. Systems 345 (1990) 295-324. | MR | Zbl
and ,30. On some methods for solving fractional programming problems with inexact data. Stud. Cerc. Mat. 45 (1993) 517-532. | MR | Zbl
and ,31. On a method for fractional optimization problems. Application to stochastic optimization problems, in Proc. of the Computer Science Conference. Svékesfehérvar, Hungary (1973) 351-355.
,32. On some procedure for solving fractional max-min problems. Rev. Anal. Numér. Théor. Approx. 17 (1988) 73-91. | MR | Zbl
,33. The minimum-risk approach for continuous time linear-fractional programming, Report No. 84. Universita di Pisa, Dipartimento di Statistica e Matematica Applicata All'Economia, Pisa (1994).
and ,34. Methods for solving stochastic bilinear fractional max-min problems. RAIRO Oper. Res. 30 (1996) 81-98. | Numdam | MR | Zbl
and ,35. A duality theorem for a class of continuous linear programming problems. SIAM J. Appl. Math. 13 (1965) 644-666. | MR | Zbl
,36. On two duality theorems for continuous programming problems. 7. Math. Anal. Appl. 31 (1970) 6-14. | MR | Zbl
,37. Duality for a class of continuous-time homogeneous fractional programming problems. Z. Oper. Res. Ser. A-B 30 (1986) 43-48. | MR | Zbl
,38. Optimality conditions and duality models for a class of nonsmooth constrained fractional optimal control problems. J. Math. Anal. Appl. 210 (1997) 114-149. | MR | Zbl
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