Finite Termination of Inexact Proximal Point Algorithms in Hilbert Spaces

Abstract

In the present paper, we study the finite termination of sequences generated by inexact proximal point algorithms for finding zeroes of a maximal monotone (set-valued) operator T on a Hilbert space. Under some mild conditions, we get that a sequence generated by inexact proximal point algorithm stops after a finite number of iterations. Our results extend the corresponding results in Rockafellar (SIAM J Control Optim 14:877-898, 1976). In particular, for optimization problems, our results improve corresponding results in Ferris (Math Progr 50:359-366, 1991). As applications, we obtain finite termination of projected gradient method.Communicated by Viorel Barbu.

Influence of Impregnation and Ion Exchange Sequence on Metal Localization, Acidity and Catalytic Performance of Cobalt BEA Zeolite Catalysts in Fischer‐Tropsch Synthesis

“…CoH/HBEA was less selective to the C 5+ hydrocarbons followed by Co/HBEA, Co/NaBEA and CoH/NaBEA, respectively with 48.7, 63.9, 66 and 71.9 %. The C 2 –C 4 olefins to paraffins ratio (Table ) show slight differences between the samples ,…”

Promotion of hydrogenation activity and sulfur resistance over Ni/ASA catalyst by support modification simultaneously with P and USY

“…As observed from Table 2, a larger amount of acid sites, particularly for Brønsted acid sites are formed on Cat-10USY. As Aguayo 42 and Wang 43 reported, Brønsted acid sites could promote the hydrogenation of aromatics. Combining XRD and TEM results, we observe that the nickel particles size over the USY modied catalyst is smaller, which could increase the surface area of the active sites.…”

Weak Sharp Minima for Interval-Valued Functions and its Primal-Dual Characterizations Using Generalized Hukuhara Subdifferentiability

“…It is known that WSM plays an important role in the sensitivity analysis and convergence analysis of conventional optimization problems [5,11,42]. It is also seen that many algorithms exhibit finite termination at WSM [5,11,27,36,42]. Motivated by these properties and wide applications of WSM in conventional optimization, in this article, we attempt to propose and mathematically characterize the notion of WSM for convex IVFs.…”