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Zbl 0987.90067
He, Y.R.
Minimizing and stationary sequences of convex constrained minimization problems. (English)
[J] J. Optimization Theory Appl. 111, No.1, 137-153 (2001). ISSN 0022-3239; ISSN 1573-2878/e

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.

MSC 2000:: *90C25 Convex programming

Keywords: constrained convex minimization; convexity; metrical regularity; minimizing sequences; stationary sequences; Moreau-Yosida regularization

Cited in: Zbl 1118.65064

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