Annals of Operations Research

, Volume 34, Issue 1, pp 107–124 | Cite as

Implicitly defined optimization problems

  • Anura H. deSilva
  • Garth P. McCormick


This paper considers the solution of the problem: inff[y, x(y)] s.t.y\(\bar R\)[y, x(y)] ⊆E k , wherex(y) solves: minF(x, y) s.t.xR(x, y) ⊆E n . In order to obtain local solutions, a first-order algorithm, which uses {dx(y)/dy} for solving a special case of the implicitly definedy-problem, is given. The derivative is obtained from {dx(y, r)/dy}, wherer is a penalty function parameter and {x(y, r)} are approximations to the solution of thex-problem given by a sequential minimization algorithm. Conditions are stated under whichx(y, r) and {dx(y, r)/dy} exist. The computation of {dx(y, r)/dy} requires the availability of ∇ y F(x, y) and the partial derivatives of the other functions defining the setR(x, y) with respect to the parametersy.


Partial Derivative Function Parameter Penalty Function Local Solution Minimization Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1992

Authors and Affiliations

  • Anura H. deSilva
    • 1
  • Garth P. McCormick
    • 2
  1. 1.Arthur D. Little, Inc.Washington, DCUSA
  2. 2.George Washington UniversityWashington, DCUSA

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