Minimizing and stationary sequences of convex constrained minimization problems. (English) Zbl 0987.90067

He, Y. R.

J. Optimization Theory Appl. 111, No. 1, 137-153 (2001).

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

Keywords:

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

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