Abstract
We consider the boundary control of a nonlinear elliptic partial differential equation with an integral performance criterion. By means of a well-known process of embedding, this problem is replaced by another, in which we seek to minimize a linear form over a subset of the product of two measure spaces defined by linear equalities. This minimization is global, and the theory allows the development of a computational method consisting of the solution of large finite-dimensional linear programming problems. Nearly optimal controls can thus be constructed. An example is given.
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