ISSN:
1572-9338
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract 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.x ∈R(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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02098175
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