The Problem of Bolza with Equality Constraints

  • Mohamed Ali El-Hodiri


We shall state, here, some theorems that characterize solutions to the problem of Bolza in the calculus of variations. The proofs of some of these theorems will only be briefly outlined. The reader may refer to Bliss (1930), (1938), and (1946) and to Pars (1962) for a more detailed presentation. By way of introduction we discuss an unconstrained problem in the calculus variation, in section 1. In section 2, we state the problem of Bolza. In section 3 we discuss first order necessary conditions and in section 4 we state the necessary conditions of Weierstrass, Clebsch, and Mayer. In section 5, we state second order sufficient conditions. In section 6, we characterize solutions to problem A’.


Transversality Condition Permanent Income Unconstrained Problem Admissible Representation Weak Neighborhood 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1991

Authors and Affiliations

  • Mohamed Ali El-Hodiri
    • 1
  1. 1.Department of EconomicsUniversity of KansasLawrenceUSA

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