caa a22 4500 475769813 CHVBK 20180406123616.0 cr unu---uuuuu 170329e20000801xx s 000 0 eng 10.1007/s101070050020 doi (NATIONALLICENCE)springer-10.1007/s101070050020 Luo Zhi-Quan Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4K1, e-mail: luozq@mcmail.cis.mcmaster.ca, CA aut New error bounds and their applications to convergence analysis of iterative algorithms [Elektronische Daten] [Zhi-Quan Luo] Abstract. : We present two new error bounds for optimization problems over a convex set whose objective function f is either semianalytic or γ-strictly convex, with γ≥1. We then apply these error bounds to analyze the rate of convergence of a wide class of iterative descent algorithms for the aforementioned optimization problem. Our analysis shows that the function sequence {f(x k )} converges at least at the sublinear rate of k -ε for some positive constant ε, where k is the iteration index. Moreover, the distances from the iterate sequence {x k } to the set of stationary points of the optimization problem converge to zero at least sublinearly. Springer-Verlag Berlin Heidelberg, 2000 Mathematical Programming Springer-Verlag 88/2(2000-08-01), 341-355 0025-5610 88:2<341 2000 88 10107 https://doi.org/10.1007/s101070050020 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s101070050020 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Luo Zhi-Quan Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4K1, e-mail: luozq@mcmail.cis.mcmaster.ca, CA aut NATIONALLICENCE 773 0- Mathematical Programming Springer-Verlag 88/2(2000-08-01), 341-355 0025-5610 88:2<341 2000 88 10107 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer