A useful approximation scheme for Lagrangians

  • E. J. Balder
Contributed Papers
  • 43 Downloads

Abstract

We present a new, useful approximation scheme for the integrand of an integral functional, revolving around a generalized bipolarity result. This scheme leads immediately to lower semicontinuity and lower closure results for the integral functional, as well as to other, more general seminormality properties.

Key Words

Semicontinuity seminormality integral functionals calculus of variations optimal control theory generalized conjugation generalized polarity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balder, E. J.,An Extension of Duality-Stability Relations to Nonconvex Optimization Problems, SIAM Journal on Control and Optimization, Vol. 15, pp. 329–343, 1977.Google Scholar
  2. 2.
    Balder, E. J.,On Seminormality of Integral Functionals and Their Integrands, SIAM Journal on Control and Optimization, Vol. 24, pp. 95–121, 1986.Google Scholar
  3. 3.
    Dolecki, S., andKurcyusz, S.,On Φ-Convexity in Extremal Problems, SIAM Journal on Control and Optimization, Vol. 16, pp. 277–300, 1978.Google Scholar
  4. 4.
    Balder, E. J.,On a Useful Compactification for Optimal Control Problems, Journal of Mathematical Analysis and Applications, Vol. 72, pp. 391–398, 1979.Google Scholar
  5. 5.
    Balder, E. J.,A General Approach to Lower Semicontinuity and Lower Closure in Optimal Control Theory, SIAM Journal on Control and Optimization, Vol. 22, pp. 570–598, 1984.Google Scholar
  6. 6.
    Clarke, F. H.,Optimization and Nonsmooth Analysis, Wiley, New York, New York, 1983.Google Scholar
  7. 7.
    Laurent, P. J.,Approximation et Optimisation, Hermann, Paris, France, 1972.Google Scholar
  8. 8.
    Castaing, C., andValadier, M.,Convex Analysis and Measurable Multifunctions, Springer Verlag, Berlin, West Germany, 1977.Google Scholar
  9. 9.
    Rockafellar, R. T.,Existence Theorems for General Control Problems of Bolza and Lagrange, Advances in Mathematics, Vol. 15, pp. 312–333, 1975.Google Scholar
  10. 10.
    Ioffe, A. D., andTichomirov, V. M.,Theory of Extremal Problems, Nauka, Moscow, USSR, 1974.Google Scholar
  11. 11.
    Balder, E. J.,Lower Closure for Orientor Fields by Lower Semicontinuity of Outer Integral Functionals, Annali di Matematica Pura ed Applicata (IV), Vol. 139, pp. 349–360, 1985.Google Scholar
  12. 12.
    Dellacherie, C., andMeyer, P. A.,Probabilités et Potentiel, Hermann, Paris, France, 1975.Google Scholar
  13. 13.
    Balder, E. J.,Short Proof of an Existence Result of V. L. Levin, Bulletin of the Polish Academy of Sciences (to appear).Google Scholar
  14. 14.
    Balder, E. J.,On Infinite-Horizon Lower Closure Results for Optimal Control, Annali di Matematica Pusa ed Applicala (IV), Vol. 151, pp. 239–246, 1988.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • E. J. Balder
    • 1
  1. 1.Department of MathematicsUniversity of UtrechtUtrechtHolland

Personalised recommendations