Trends in Applications of Mathematics to Mechanics by Elisabetta Rocca Ulisse Stefanelli Lev Truskinovsky & Augusto Visintin

Author:Elisabetta Rocca, Ulisse Stefanelli, Lev Truskinovsky & Augusto Visintin
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

i.e., the residual is non-increasing.

Proof

The optimality conditions for a saddle-point of are given by

(9)

and p h  = ∇z h and s h  = z h . On the other hand, with and , the optimality conditions for the iterates of Algorithm 3.1 read

(10)

Testing (9) and (10) with and , respectively, and adding corresponding inequalities gives

The rest of the proof of the first estimate is analogous to the proof of [5, Thm. 3.7].

The proof of the monotonicity follows by testing (10) at iterations j and j + 1 with and , respectively, and adding the inequalities, which gives

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.