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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 $\bbfR^n$, one can consider the corresponding problem of minimizing a smooth convex function $F$ on $\bbfR^n$, 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.

90C25Convex programming
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