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Zbl 0863.49018
Lehdili, N.; Moudafi, A.
Combining the proximal algorithm and Tikhonov regularization. (English)
[J] Optimization 37, No.3, 239-252 (1996). ISSN 0233-1934; ISSN 1029-4945/e

Let $X$ be a real Hilbert space and $T:X\to 2^X$ a multivalued maximal monotone operator. The authors consider the following problem: $$\text{find }x\in X\text{ such that }0\in T(x).$$ They present an approximation method which combines the Tikhonov regularization with the proximal point algorithm. The convergence of the method is established. A particular attention is given to convex and convex-concave optimization problems.
[G.Vainikko (Espoo)]

MSC 2000:: *90C25 Convex programming
90C48 Programming in abstract spaces
65J20 Improperly posed problems (numerical methods in abstract spaces)

Keywords: maximal monotone operators; Tikhonov regularization; proximal point algorithm

Cited in: Zbl 1214.49009

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