Skip to main content
Log in

Regularity conditions for constrained extremum problems

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Necessary and/or sufficient conditions are stated in order to have regularity for nondifferentiable problems or differentiable problems. These conditions are compared with some known constraint qualifications.

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. Giannessi, F.,Theorems of the Alternative and Optimiality Conditions, Journal of Optimization Theory and Applications, Vol. 42, No. 3, 1984.

  2. Bazaraa, M. S., andShetty, C. M.,Foundations of Optimization, Springer-Verlag, Berlin, Germany, 1976.

    Google Scholar 

  3. Abadie, J.,Nonlinear Programming, North-Holland Publishing Company, Amsterdam, Holland, pp. 21–36, 1967.

    Google Scholar 

  4. Arrow, K. J., Hurwicz, L., andUzawa, H.,Constraint Qualifications in Maximization Problem, Naval Research Logistics Quarterly, Vol. 8, pp. 175–191, 1961.

    Google Scholar 

  5. Borwein, J.,Multivalued Convexity and Optimization: A Unified Approach to Inequality and Equality Constraints, Mathematical Programming, Vol. 13, pp. 183–199, 1977.

    Google Scholar 

  6. Cambini, A.,Sulla Regolarità nei Problemi di Estremo Vettoriale, University of Pisa, Department of Mathematics, Optimization and Operations Research Section, Paper No. A-98, 1982.

  7. Clarke, F. H.,A New Approach to Lagrange Multiplers, Mathematics of Operations Research, Vol. 1, pp. 165–174, 1976.

    Google Scholar 

  8. Giannessi, F.,Theorems of Alternative, Quadratic Programs, and Complementarity Problems. Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, John Wiley and Sons, New York, New York, 1980.

    Google Scholar 

  9. Gould, F. J., andTolle, J. W.,A Necessary and Sufficient Qualification for Constrained Optimization, SIAM Journal on Applied Mathematics, Vol. 20, pp. 164–172, 1971.

    Google Scholar 

  10. Martein, L.,A Necessary and Sufficient Regularity Condition for Convex Extremum Problems, University of Pisa, Department of Mathematics, Optimization and Operations Research Section. Paper No. A-90, 1982.

  11. Robinson, S. M.,Stability Theory for Systems of Inequalities, Part 2: Differentiable Nonlinear Systems, SIAM Journal on Numerical Analysis, Vol. 13, pp. 497–513, 1976.

    Google Scholar 

  12. Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1969.

    Google Scholar 

  13. Clarke, F. M.,Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, New York, 1983.

    Google Scholar 

  14. Pshenichnyi, B. N.,Necessary Conditions for an Extremum, Marcel Dekker, New York, New York, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by I. Galligani

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martein, L. Regularity conditions for constrained extremum problems. J Optim Theory Appl 47, 217–233 (1985). https://doi.org/10.1007/BF00940770

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00940770

Key Words

Navigation