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A saddle-point criterion for convex problems with infinite-dimensional equality constraints

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Abstract

In this paper, we develop a saddle-point criterion for convex optimization problems with infinite-dimensional equality constraints. The method used in the derivation of this criterion is based on the property of openness of the equality operator. As an application, we develop necessary and sufficient conditions for an optimal control problem under a suitable controllability assumption. Constructing an optimal solution for a production planning problem is used as an illustrative example.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia

    M. S. Bazaraa (Associate Professor)

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia

    J. J. Goode (Associate Professor)

Authors
  1. M. S. Bazaraa
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  2. J. J. Goode
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Additional information

Communicated by A. Miele

The authors would like to thank Professor R. T. Rockafellar for his suggestions which have resulted in an improved version of the paper.

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Bazaraa, M.S., Goode, J.J. A saddle-point criterion for convex problems with infinite-dimensional equality constraints. J Optim Theory Appl 17, 115–131 (1975). https://doi.org/10.1007/BF00933918

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  • DOI: https://doi.org/10.1007/BF00933918

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