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Minimizing and stationary sequences of convex constrained minimization problems. (English) Zbl 0987.90067
Summary: In the asymptotic analysis of the minimization problem for a nonsmooth convex function on a closed convex set $$X$$ in $$\mathbb{R}^n$$, one can consider the corresponding problem of minimizing a smooth convex function $$F$$ on $$\mathbb{R}^n$$, where $$F$$ denotes the Moreau-Yosida regularization of $$f$$. We study the interrelationship between the minimizing/stationary sequence for $$f$$ and that for $$F$$. An algorithm is given to generate iteratively a possibly unbounded sequence, which is shown to be a minimizing sequence of $$f$$ under certain regularity and uniform continuity assumptions.

##### MSC:
 90C25 Convex programming
Full Text:
##### References:
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