«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2009. Vol. 1

Qausi-convex programming

Author(s)
R. Enkhbat
Abstract

This paper considers problems of maximization and minimization of quasiconvex function at arbitrary set. Global optimality conditions are formulated.

Keywords
non-convex optimization, global searching
UDC
519.583
References

1. Takayama A. Mathematical Economics / A.Takayama. —Cambridge University Press, 1985.

2. Jaumard B. Generalized Convex Multiplicative Programming via Quasiconcave Minimization / B. Jaumard, C. Meyer, H. Tuy // Journal of Global Optimization. — 1997. — № 10. — P. 229–256.

3. Bulatov V.P. The Embedding Methods in Extremum Problems/ V.P. Bulatov. — Novosibirsk: Nauka, 1977.

4. DixitA. K.Optimizationin Economic Theory/ A. K.Dixit. — Oxford University Press, 1976.

5. Katzner D. W.Static Demand Theory/ D. W. Katzner. —Macmillian, London, 1970.

6. Katzner D. W. Walrasian Microeconomics / D. W. Katzner. — Addison-Wesley, New-York, 1988.

7. Enkhbat R. An Algorithm for Maximizing a Convex Function over a Simple Set/ R. Enkhbat // Journal of Global Optimization. —1996.№8. —P.379–391.

8. Harold P. B. An Outcome Space Branch and Bound-Outer Approximation Algorithm for Convex Multiplicative Programming / P. B. Harold // Journal of Global Optimization. — 1999. — № 15. — P. 315–342.

9. Hiriart-Urruty J. B. From Convex Optimization to Nonconvex Optimization / J. B.Hiriart-Urruty// Nonsmooth Optimization and Related Topics, Plenum. — 1989. — P. 219–239.

10. Hiriart-Urruty J. B. A Note on the Characterization of the Global Maxima of a (tangentially) Convex Function over a Convex Set / J. B. Hiriart-Urruty, J.S.Ledyaev// Journal of Convex Analysis. —1996. —Vol.3,№1. —P.55–61.

11. Horst R. On the Global Minimization of a Concave Function: Introduction and Servey/ R.Horst// Operations Research Spectrum. —1984.№6. —P.195–200.

12. Horst R. A General Class of Branch and Bound Methods in Global Optimization with some New Approaches for Concave Minimization / R. Horst // Journal of Optimization Theory and Applications. — 1986. — № 51. P. 271–291.

13. Horst R. Outer Cut Methods in Global Optimization/ R.Horst// Lecture Notes in Economics and Mathematical Systems, 1987. — Vol. 304. — P. 28–40.

14. HorstR.OuterApproximationbyPolyhedralConvexSets/R.Horst,N.V.Thoai, H.Tuy// Operations Research Spectrum. —1987. —Vol.9.,№3. —P.153–159.

15. Horst R. A New Branch and Bound Approach for Concave Minimization Problems/ R.Horst// Lecture Notes in Computer Science. — 1987. — Vol.41. — P.330–337.

16. Horst R. Global Optimization(Deterministic Approaches) / R. Horst, H. Tuy. — Springer, Berlin, 1990.

17. James M. H. Microeconomic theory: A Mathematical Approach / M. H. James, E.Q.Richard. —McGraw-Hill,1971.

18. Kantorovich L. V. On an Effective Method for Solving some Classes of Extremum probelms/ L.V. Kantorovich// Soviet Math. Doklady. — 1940. — Vol.28,№3. — P. 212–215.

19. Konno H. Multiplicative Programming Problems / H. Konno, T. Kuno // Handbook of Global Optimization. — Kluwer Dordrecht. — 1995. — P. 369–405.

20. Michael D.I. Mathematical Optimization and Economic Theory/ D.I.Michael. — Prentice-Hall, 1971.

21. Pardalos P.M. Constrained Global Optimization: Algorithms and Applications/ P.M.Pardalos, J. B.Rosen// Lecture Notes in Computer Science. —1987.

22. Pardalos P. M. Methods for Global Concave Minimization: A Bibliographic Survey / P. M. Pardalos, J. B. Rosen // SIAM Review. — 1986. — № 28. — P. 367–379.

23. Madden P., Concavity and Optimization in Microeconomics /P.Madden. — Oxford University Press, 1986.

24. Rockafellar R. T. Convex Analysis / R. T. Rockafellar. — Princeton University Press, Princeton, 1970.

25. Weintraub R. E. Mathematics for Economists / R. E. Weintraub. — Cambridge University Press, 1982.

26. Schaible S. Invited Review: Fractional programming / S. Schaible, T. Ibaraki // European J. of Operational Research. — 1983. — № 12. — P. 325–338.

27. Strekalovsky A.S. On the Global Extremum Problem / A.S.Strekalovsky//Soviet Math. Doklady. — Vol. 292, № 5. — P. 1062–1066.

28. Strekalovsky A. S. Global Optimality Conditions for Nonconvex Optimization / A. S. Strekalovsky // Journal of Global Optimization. — 1998. — № 12. — P. 415–434.

29. Tuy H. Concave Programming under Linear Constraints / H. Tuy // Soviet Math.Doklady. — 1964. — Vol. 159, № 1. — P. 32–35.

30. Tuy H. Normal Conical Algorithm for Concave Minimization over Polytopes / H.Tuy// Mathematical Programming. —1991. —№51. —P.229–245.

31. Varian H.R. Microeconomic Analysis/ H.R.Varian. —Norton,New-York,1984.

32. Vasiliev O. V. Optimization Methods / O. V. Vasiliev. — World Federation Publishers, Atlanta, 1996.


Full text (russian)