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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


On the free boundary of a quasivariational inequality arising in a problem of quality control

Author: Avner Friedman
Journal: Trans. Amer. Math. Soc. 246 (1978), 95-110
MSC: Primary 93E20; Secondary 49A29, 62N10
MathSciNet review: 515531
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Abstract: In some recent work in stochastic optimization with partial observation occurring in quality control problems, Anderson and Friedman [1], [2] have shown that the optimal cost can be determined as a solution of the quasi variational inequality

\begin{displaymath}\begin{gathered}Mw\left( p \right)\, + \,f\left( p \right)\, ... ... \,\psi \left( {p;\,w} \right)} \right)\, = \,0 \end{gathered} \end{displaymath}

in the simplex $ {p_i}\, > \,0$, $ \sum\nolimits_{i\, = \,1}^n {{p_i}\, = \,1} $. Here f, $ \psi $ are given functions of p, $ \psi $ is a functional of w, and M is a given elliptic operator degenerating on the boundary. This system has a unique solution when M does not degenerate in the interior of the simplex. The aim of this paper is to study the free boundary, that is, the boundary of the set where $ w\left( p \right)\, < \,\psi \left( {p;\,w} \right)$.

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PII: S 0002-9947(1978)0515531-6
Article copyright: © Copyright 1978 American Mathematical Society