Skip to main content
SpringerLink
Log in

Sufficient conditions and sensitivity analysisfor economic control problems

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Second‐order sufficient optimality conditions for nonlinear optimal control problems arereviewed. Applications of these conditions to convex‐concave models of economic controlare presented. On the basis of second‐order conditions, recent stability results are discussedthat ensure differentiability of optimal solutions with respect to perturbation parameters inthe system. Methods for computing the sensitivity differentials of optimal solutions areoutlined and numerical results for two economic control problems are given.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ch. Büskens and H. Maurer, Sensitivity analysis and real-time control of nonlinear optimal control problems via nonlinear programming methods, Proceedings of the 12th Conference on Calculus of Variations, Optimal Control and Applications, Trassenheide, Germany, September 23-27, 1996, International Series of Numerical Mathematics, vol. 124, Birkhäuser, Basel, 1998, pp. 185-196.

    Google Scholar 

  2. A.L. Dontchev and W.W. Hager, Lipschitz stability in nonlinear control and optimization, SIAM J. Control and Optimization 31(1993)569-603.

    Google Scholar 

  3. A.L. Dontchev, W.W. Hager, A.B. Poore and B. Yang, Optimality, stability and convergence in nonlinear control, Applied Mathematics and Optimization 31(1995)297-326.

    Google Scholar 

  4. G. Feichtinger and R.F. Hartl, Optimale Kontrolle ökonomischer Prozesse, Walter de Gruyter, Berlin, 1986.

    Google Scholar 

  5. K. Malanowski, Stability and sensitivity of solutions to nonlinear optimal control problems, Applied Mathematics and Optimization 32(1995)111-141.

    Google Scholar 

  6. K. Malanowski and H. Maurer, Sensitivity analysis for parametric control problems with control-state constraints, Computational Optimization and Applications 5(1996)253-283.

    Google Scholar 

  7. K. Malanowski and H. Maurer, Sensitivity analysis for state constrained control problems, Discrete and Continuous Dynamical Systems 4(1998)241-272.

    Google Scholar 

  8. H. Maurer, First and second order sufficient optimality conditions in mathematical programming and optimal control, Mathematical Programming Study 14(1981)163-177.

    Google Scholar 

  9. H. Maurer and D. Augustin, Second order sufficient conditions and sensitivity analysis for the controlled Rayleigh problem, in: Proceedings of the International Conference on Parametric Optimization and Related Topics IV, Enschede, June 6-9, 1995, eds. J. Guddat, H.Th. Jongen, F. Nožička, G. Still and F. Twilt, Peter Lang, 1996, pp. 245-259.

  10. H. Maurer, Ch. Büskens and G. Feichtinger, Solution techniques for periodic control problems: A case study in production planning, Optimal Control Applications and Methods 19(1998)185-203.

    Google Scholar 

  11. H. Maurer and H.J. Pesch, Solution differentiability for parametric nonlinear control problems, SIAM J. on Control and Optimization 32(1994)1542-1554.

    Google Scholar 

  12. H. Maurer and H.J. Pesch, Solution differentiability for parametric nonlinear control problems with control-state constraints, J. of Optimization Theory and Applications 86(1995)285-309.

    Google Scholar 

  13. H. Maurer and S. Pickenhain, Second order sufficient conditions for optimal control problems with mixed control-state constraints, J. of Optimization Theory and Applications 86(1995)649-667.

    Google Scholar 

  14. H.J. Oberle and W. Grimm, BNDSCO — A program for the numerical solution of optimal control problems, Institute for Flight Systems Dynamics, DLR, Internal Report No. 515-89/22, Oberpfaffenhofen, Germany, 1989.

    Google Scholar 

  15. S. Pickenhain, Sufficiency conditions for weak local minima in multidimensional optimal control problems with mixed control-state restrictions, Zeitschrift für Analysis und ihre Anwendungen 11 (1992)559-568.

    Google Scholar 

  16. N.P. Osmolovskii, Quadratic conditions for nonsingular extremals in optimal control (a theoretical treatment), Russian J. of Mathematical Physics 2(4)(1995)487-516.

    Google Scholar 

  17. G. Sorger, Sufficient conditions for nonconvex control problems with state constraints, J. of Optimization Theory and Applications 62(1989)289-310.

    Google Scholar 

  18. Q. Wang and J.L. Speyer, Necessary and sufficient conditions for local optimality of a periodic process, SIAM J. on Control and Optimization 28(1990)482-497.

    Google Scholar 

  19. V. Zeidan, Sufficiency conditions with minimal regularity assumption, Applied Mathematics and Optimization 20(1989)19-31.

    Google Scholar 

  20. V. Zeidan, The Riccati equation for optimal control problems with mixed state-control constraints: Necessity and sufficiency, SIAM J. Control and Optimization 32(1994)1297-1321.

    Google Scholar 

Download references

Authors
  1. H. Maurer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maurer, H. Sufficient conditions and sensitivity analysisfor economic control problems. Annals of Operations Research 88, 3–14 (1999). https://doi.org/10.1023/A:1018942732605

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018942732605

Keywords

Search

Navigation