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Calcul d’un point fixe d’une application prox par la mêthode des approximations successives; conditions de convergence finie. (Computation of a fixed point of a proximal mapping by the successive approximation method; finite convergence conditions). (French) Zbl 0607.65030
Let us consider the proximal mapping \(\Pr ox_{T_ A}=(I+T_ A)^{- 1}\) associated with the partial inverse \(T_ A\) (with respect to a subspace A) of the subdifferential T of a polyhedral convex function. In this note we give sufficient conditions which imply the finite convergence of the successive approximation method for computing a fixed point of \(\Pr ox_{T_ A}\). Using examples we show how these conditions can be realized and we give a case with non finite termination.

65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
65K05 Numerical mathematical programming methods
90C25 Convex programming
47H05 Monotone operators and generalizations
47H10 Fixed-point theorems
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49J40 Variational inequalities