Skip to main content
Log in

Solving cone-constrained convex programs by differential inclusions

  • Published:
Mathematical Programming Submit manuscript

Abstract

A differential inclusion is designed for solving cone-constrained convex programs. The method is of subgradient-projection type. It involves projection, penalties and Lagrangian relaxation. Nonsmooth data can be accommodated. A novelty is that multipliers converge monotonically upwards to equilibrium levels. An application to stochastic programming is considered.

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. K.J. Arrow, L. Hurwicz and H. Uzawa,Studies in Linear and Non-linear Programming (Stanford University Press, Stanford, 1958).

    Google Scholar 

  2. J.P. Aubin and A. Cellina,Differential Inclusions (Springer-Verlag, Berlin, 1984).

    Google Scholar 

  3. D.P. Bertsekas,Constrained Optimization and Lagrange Multiplier Methods (Academic Press, New York, 1982).

    Google Scholar 

  4. Y. Evtushenko, “Generalized Lagrange multiplier techniques for nonlinear programming,”Journal on Optimization Theory and Applications 21 (1977) 121–135.

    Google Scholar 

  5. S.D. Flåm and A. Ben-Israel, “Approximating saddle points as equilibria of differential inclusions,”Journal on Optimization Theory and Applications 141 (1989) 264–277.

    Google Scholar 

  6. S.D. Flåm and J. Zowe. “A primal-dual differential method for convex programming,” in: A. Ioffe et al., eds.,Optimization and Nonlinear Analysis (Pitman Research Notes in Math. 244, 1992) 119–129.

  7. S.D. Flåm, “Paths to constrained Nash equilibria,”Applied Mathematics and Optimization 27 (1993) 275–289.

    Google Scholar 

  8. G. Isac and A.B. Nemeth, “Every generating isotone projection cone is latticial and correct,”Journal of Mathematical Analysis and Applications 147 (1990) 53–62.

    Google Scholar 

  9. G. Isac and A.B. Nemeth, “Isotone projection cones in Hilbert spaces and the complementarity problem,”Unione Matematica Italiana. Bolletino 7 (1990) 773–802.

    Google Scholar 

  10. V.G. Karmanov,Mathematical Programming (MIR Publishers, Moscow, 1989).

    Google Scholar 

  11. R.T. Rockafellar, “Integrals which are convex functionals,”Pacific Journal of Mathematics 24 (1968) 525–539.

    Google Scholar 

  12. R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, N.J., 1970).

    Google Scholar 

  13. R.T. Rockafellar, “Monotone operators associated with saddle-functions and minimax problems,” in: F.E. Browder, ed.,Nonlinear Functional Analysis (Proceedings of Symposia in Pure Mathematics, Vol. 18, Part 1, 1970) 241–250.

    Google Scholar 

  14. R.T. Rockafellar, “Integrals which are convex functionals, Part II,”Pacific Journal of Mathematics 39 (1971) 439–469.

    Google Scholar 

  15. H.H. Schaefer,Topological Vector Spaces, Graduate Texts in Mathematics 3 (Springer-Verlag, Berlin, 1971).

    Google Scholar 

  16. V.I. Venets, “Continuous algorithms for solution of convex optimization problems and finding saddle points of convex—concave functions with the use of projection operations,”Optimization 16 (1985) 519–533.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Corresponding author.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Flåm, S.D., Seeger, A. Solving cone-constrained convex programs by differential inclusions. Mathematical Programming 65, 107–121 (1994). https://doi.org/10.1007/BF01581692

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01581692

AMS Subject Classification

Keywords

Navigation