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Combining the proximal algorithm and Tikhonov regularization. (English) Zbl 0863.49018

Let $X$ be a real Hilbert space and $T:X\to {2}^{X}$ a multivalued maximal monotone operator. The authors consider the following problem:

$\text{find}\phantom{\rule{4.pt}{0ex}}x\in X\phantom{\rule{4.pt}{0ex}}\text{such}\phantom{\rule{4.pt}{0ex}}\text{that}\phantom{\rule{4.pt}{0ex}}0\in T\left(x\right)·$

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.

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