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On state constrained optimal shape design problems. (English) Zbl 0637.49003

Optimal control of partial differential equations II: theory and applications, Conf. Oberwolfach/Ger. 1986, ISNM 78, 109-122 (1987).
[For the entire collection see Zbl 0597.00023.]
The authors discuss the existence of optimal pairs for the problem of the type: \[ Minimize\quad I(y,u)\quad subject\quad to\quad A(u)y+\quad \partial \phi (y)\ni Bu\quad +f,\quad y\in K,\quad u\in U_ a, \] where \(A(u):V\to V'\) is a linear continuous operator, \(\phi\) :V\(\to (- \infty,\infty]\), a convex, lower semi-continuous, proper function. \(U_ a\subset U\) and \(K\subset V\) are closed convex sets, \(f\in V'\), B:U\(\to V\), a linear continuous operator. Here U, V are Banach spaces, \(V'\) is the dual of V. A variational inequality approach is applied to the finite dimension optimal design problem. Several examples are given to illustrate the results.
Reviewer: M.A.Noor

MSC:

49J27 Existence theories for problems in abstract spaces
49J20 Existence theories for optimal control problems involving partial differential equations
49J40 Variational inequalities
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)

Citations:

Zbl 0597.00023