Journal of Optimization Theory and Applications

, Volume 71, Issue 3, pp 549–568 | Cite as

Euler-Lagrange equation in the case of nonregular equality constraints

  • U. Ledzewicz-Kowalewska
Contributed Papers


An optimization problem with inequality and equality constraints in Banach spaces is considered in the case when the operators which determine the equality constraints are nonregular. In this case, the classical Euler-Lagrange equation has the degenerate form, i.e., does not depend on the functional to be minimized. Applying some generalization of the Lusternik theorem to the Dubovitskii-Milyutin method, the family of Euler-Lagrange equations is obtained in the nondegenerate form under the assumption of twice Fréchet differentiability of the operators. The Pareto-optimal problem is also considered.

Key Words

Dubovitskii-Milyutin method Euler-Lagrange equation equality constraints nonregular operators Lusternik theorem Pareto optimality 


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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • U. Ledzewicz-Kowalewska
    • 1
  1. 1.Department of Mathematics and StatisticsSouthern Illinois University at EdwardsvilleEdwardsville

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