no. 4
Continuous time linear-fractional programming. The minimum-risk approach
RAIRO - Operations Research - Recherche Opérationnelle, Tome 34 (2000) no. 4, pp. 397-409. 
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     pages = {397--409},
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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://www.numdam.org/item/RO_2000__34_4_397_0/

1. E.J. Anderson and A.B. Philpott, On the solution of a class of continuous linear programs. SIAM J. Control Optim. 32 (1994) 1289-1296. | MR | Zbl

2. K.M. Anstreicher, 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. R. Bellman, Bottleneck problems and dynamic programming. Proc. Nat Acad. Sci. 39 (1953) 947-951. | MR | Zbl

4. R. Bellman, Dynamic Programming. Princeton University Press, Princeton, NJ (1957). | MR | Zbl

5. B. Bereanu, On stochastic linear programming, I: Distribution problems: A single random variable. Rev. Roumaine Math. Pures Appl. 8 (1963) 683-697. | MR | Zbl

6. B. Bereanu, Programme de risque minimal en programmation linaire stochastique. C. R. Acad. Sci. Paris 259 (1964) 981-983. | MR | Zbl

7. E.P. Bodo and M.A. Hanson, A class of continuous time programming problems. J. Optim. Theory Appl. 24 (1978) 243-263. | MR | Zbl

8. R.N. Buie, J. Abrham, Numerical solutions to continuous linear programming problems. Oper. Res. 17 (1973) 107-117. | MR | Zbl

9. A. Charnes, W.W. Cooper, Deterministic equivalents for optimizing and satisfying under chance constraints. Oper. Res. 11 (1963) 18-39. | MR | Zbl

10. W. Dinkelbach, On nonlinear fractional programming. Management Sci. 13 (1967) 492-498. | MR | Zbl

11. W.P. Drews, 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. W.H. Farr and M.A. Hanson, Continuous time programming with nonlinear time-delayed constraints. J. Math. Anal. Appl. 46 (1974) 41-61. | MR | Zbl

13. M.A. Hanson and B. Mond, A class of continuous convex programming problems. J. Math. Anal. Appl. 22 (1968) 427-437. | MR | Zbl

14. R J. Hartberger, 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. B. Johannesson and M.A. Hanson, 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

16. B. Johannesson and M.A. Hanson, 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).

17. A.F. Perold, Fundamentals of a continuous time simplex method,, Tech. Report SOL 78-26. Department of Opérations Research, Stanford University, Stanford, CA (1978).

18. M. Pullan, An algorithm for a class of continuous linear programs. SIAM J. Control Optim. 31 (1993) 1558-1577. | MR | Zbl

19. M.C. Pullan, Forms of optimal solutions for separated continuous linear programs. SIAM J. Control Optim. 33 (1995) 1952-1977. | MR | Zbl

20. R.G. Segers, 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. C. Singh, Continuous time programming with set-inclusive constraints and objective set. J. Math. Anal. Appl. 91 (1983) 367-375. | MR | Zbl

22. C. Singh and M. Kiran, Continuous time matrix programming. J. Math. Anal. Appl. 173 (1993) 280-291. | MR | Zbl

23. I.M. Stancu-Minasian, Stochastic Programming with Multiple Objective Functions. Editura Academiei Române, Bucuresti and D. Reidel Publishing Company, Dordrecht, Boston, Lancester (1984). | MR | Zbl

24. I.M. Stancu-Minasian, Metode de rezolvare a problemelor de programare fractionara. Editura Academiei Romane, Bucuresti (1992). | MR | Zbl

25. I.M. Stancu-Minasian, Fractional Programming. Theory, Methods and Applications. Kluwer Academic Publishers, Dordrecht/Boston/London (1997). | MR | Zbl

26. I.M. Stancu-Minasian and S. Tigan, 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

27. I.M. Stancu-Minasian and S. Tigan, 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

28. I.M. Stancu-Minasian and S. Tigan, A stochastic approach to some linear fractional goal programming problems. Kybernetika (Praha) 24 (1988) 139-149. | MR | Zbl

29. I.M. Stancu-Minasian and S. Tigan, 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

30. I.M. Stancu-Minasian and S. Tigan, On some methods for solving fractional programming problems with inexact data. Stud. Cerc. Mat. 45 (1993) 517-532. | MR | Zbl

31. S. Tigan, 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. S. Tigan, On some procedure for solving fractional max-min problems. Rev. Anal. Numér. Théor. Approx. 17 (1988) 73-91. | MR | Zbl

33. S. Tigan and I.M. Stancu-Minasian, 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).

34. S. Tigan and I.M. Stancu-Minasian, Methods for solving stochastic bilinear fractional max-min problems. RAIRO Oper. Res. 30 (1996) 81-98. | Numdam | MR | Zbl

35. W.F. Tyndall, A duality theorem for a class of continuous linear programming problems. SIAM J. Appl. Math. 13 (1965) 644-666. | MR | Zbl

36. W.F. Tyndall, On two duality theorems for continuous programming problems. 7. Math. Anal. Appl. 31 (1970) 6-14. | MR | Zbl

37. G.J. Zalmai, Duality for a class of continuous-time homogeneous fractional programming problems. Z. Oper. Res. Ser. A-B 30 (1986) 43-48. | MR | Zbl

38. G.J. Zalmai, 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