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On the rate of convergence of projected Barzilai-Borwein methods. (English) Zbl 1338.90300
Summary: We study the rate of convergence of a projected Barzilai-Borwein method, which performs the Grippo-Lampariello-Lucidi (GLL) non-monotone line search along the feasible direction, for convex constrained optimization. Under mild conditions, we establish sublinear convergence of the considered method for general convex functions. Moreover, we show that the rate of convergence is \(R\)-linear for strongly convex functions. We extend the convergence results to different versions of the method based on a general GLL non-monotone line search, an adaptive non-monotone line search, and a non-monotone line search that requires an average of the successive function values decreases.

MSC:
90C25 Convex programming
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