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Infinitely constrained optimization problems

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Abstract

A generalized cutting-plane algorithm designed to solve problems of the form min{f(x) :x ∈X andg(x,y) ∈ 0 for ally ∈Y} is described. Convergence is established in the general case (f,g continuous,X andY compact). Constraint dropping is allowed in a special case [f,g(·,y) convex functions,X a convex set]. Applications are made to a variety of max-min problems. Computational considerations are discussed.

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Authors and Affiliations

  1. Institute for Defense Analyses, Arlington, Virginia

    J. W. Blankenship (Staff Member)

  2. Department of Operations Research, The George Washington University, Washington, DC

    J. E. Falk (Associate Research Professor of Operations Research)

Authors
  1. J. W. Blankenship
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  2. J. E. Falk
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Additional information

Communicated by O. L. Mangasarian

Dr. Falk's research was supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under AFOSR Contract No. 73–2504.

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Blankenship, J.W., Falk, J.E. Infinitely constrained optimization problems. J Optim Theory Appl 19, 261–281 (1976). https://doi.org/10.1007/BF00934096

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  • DOI: https://doi.org/10.1007/BF00934096

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