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Summary: Comput. Maths. Math. Phys., Vol.35, No.5, pp. 539551, 1995
Pergamon c 1994 Elsevier Science Ltd
Printed in Great Britain. All rights reserved
0965-5425(95)00074-7
THE CONVERGENCE OF PROXIMAL METHODS
TO FIXED POINTS OF EXTREMAL MAPPINGS
AND ESTIMATES OF THEIR RATE OF CONVERGENCE1
A.S. ANTIPIN
Moscow
(Revised version 16 December 2002)
It is proved that proximal methods converge to the sharp, strongly convex, and degenerate
xed points of extremal mappings.
1. STATEMENT OF THE PROBLEM
We will consider the problem of calculating the xed point of the extremal mapping
v
Argmin{(w, v
) : w }, v , (1.1)
where the function (w, v) is dened on the square × and Rn
. We shall assume that
(w, v) is convex with respect to the variable w for each xed v. Also, the set Argmin{(w, v) :
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