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Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. (English) Zbl 1156.90426

Summary: We establish a strong convergence theorem regarding a regularized variant of the projected subgradient method for nonsmooth, nonstrictly convex minimization in real Hilbert spaces. Only one projection step is needed per iteration and the involved stepsizes are controlled so that the algorithm is of practical interest. To this aim, we develop new techniques of analysis which can be adapted to many other non-Fejérian methods.

MSC:

90C25 Convex programming
90C30 Nonlinear programming
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