Skip to main content
Log in

An algorithm for maximizing a convex function over a simple set

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

The problem of maximizing a convex function on a so-called simple set is considered. Based on the optimality conditions [19], an algorithm for solving the problem is proposed. This numerical algorithm is shown to be convergent. The proposed algorithm has been implemented and tested on a variety of test problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. BertsekasD. P. (1982),Constrained Optimization and Lagrange Multiplier methods, Academic Press, New York

    Google Scholar 

  2. BulatovV. P. (1977),The Immersion Methods in Optimization Problems, Nauka, Novosibirsk.

    Google Scholar 

  3. DemyanovV. P. and VasyelivL. V. (1981),Nondifferentiable Optimization, Nauka, Moscow.

    Google Scholar 

  4. EbtushenkoY. G. (1971), Numerical Method for Finding the Global Extremum of a Function,Journal of Numerical Methematics and Mathematical Physics 11(6), 1390–1403.

    Google Scholar 

  5. Hiriart-Urruty, J. B. (1989), From Convex Optimization to Nonconvex Optimization,Nonsmooth Optimization and Related Topics, Plenum, 219–239.

  6. HorstR. (1984), On the Global Minimization of a Concave Function: Introduction and Survey,Operations Research Spectrum 6, 195–200.

    Article  Google Scholar 

  7. HorstR., ThoaiN. V., and TuyH. (1987), Outer Approximation by Polyhedral Convex Sets,Operations Research Spectrum 9(3), 153–159.

    Article  Google Scholar 

  8. HorstR. and TuyH. (1990),Global Optimization (Deterministic Approaches), Springer, Berlin.

    Google Scholar 

  9. KalantariB. and RosenJ. B. (1987), Algorithm for Large-Scale Global Minimization of Linearly Constrained Concave Quadratic Functions,Mathematics of Operations Research 12, 544–561.

    Article  Google Scholar 

  10. KarmanovV. G. (1989),Mathematical Programming, Mir Publishers, Moscow.

    Google Scholar 

  11. Kirin, N. E. (1968),Numerical Method of the Optimal Control Theory, Leningrad.

  12. MuchaelyevichV. S., GupalA. M., and NorkinV. I. (1987),Methods of Nonconvex Optimization, Nauka, Moscow.

    Google Scholar 

  13. NefedovV. N. (1987), Finding of Global Maximum of Function of Several Variables on a Set Given by Inequality Constraints,Journal of Numerical Mathematics and Mathematical Physics 27 (1), 35–51.

    Google Scholar 

  14. Pardalos, P. M. and Rosen, J. B. (1987),Constrained Global Optimization: Algorithms and Applications. Springer-Verlag, Lecture Notes in Computer Science, 268.

  15. Podinovskii, V. V. and Timohov, A. V. (1988),Introduction to Mathematical Programming, Moscow University.

  16. ReklatisG. V., RavindranA., and RagsdellM. (1983),Engineering Optimization Methods and Applications, John Wiley and Sons, Inc., New York.

    Google Scholar 

  17. RockafellarR. T. (1970),Convex Analysis, Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  18. RosenJ. B. and PardalosP. M. (1986), Global Minimization of Large-Scale Constrained Concave Quadratic Problems by Separable Programming,Mathematical Programming 34, 163–174.

    Article  Google Scholar 

  19. StrekalovskiiA. S. (1987), On the Global Extremum Problem,Soviet Math. Doklady 292 (5), 1062–1066.

    Google Scholar 

  20. StrekalovskiiA. S. and EnhbatR. (1990),Global Maximum of Convex Functions on an Arbitrary Sets, Dep. in VINITI, 1063, Irkutsk.

    Google Scholar 

  21. TuyH. (1964), Concave Programming under Linear Constraints,Soviet Math. Doklady 159(1), 32–35.

    Google Scholar 

  22. TuyH. (1991), Normal Conical Algorithm for Concave Minimization over Polytopes,Mathematical Programming 51, 229–245.

    Article  Google Scholar 

  23. WoodG. R. (1991), Multidimensional Bisection Applied to Global Optimization,Computer Math. Applic. 21 (7), 161–172.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Enhbat, R. An algorithm for maximizing a convex function over a simple set. J Glob Optim 8, 379–391 (1996). https://doi.org/10.1007/BF02403999

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02403999

Key words

Navigation