- An induction theorem and nonlinear regularity models Phan Q. Khanh (pqkhanhusgmail.com) Alexander Y. Kruger (a.krugerfederation.edu.au) Nguyen H. Thao (hieuthaonguyenstudents.federation.edu.au) Abstract: A general nonlinear regularity model for a set-valued mapping $F:X\times\R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves. Namely, we revise the \emph{induction theorem} from Khanh, \emph{J. Math. Anal. Appl.}, 118 (1986) and employ it to obtain basic estimates for studying regularity/openness properties. We also show that it can serve as a substitution of the Ekeland variational principle when establishing other regularity criteria. Then, we apply the induction theorem and the mentioned estimates to establish criteria for both global and local versions of regularity/openness properties for our model and demonstrate how the definitions and criteria translate into the conventional setting of a set-valued mapping $F:X\rightrightarrows Y$. Keywords: metric regularity, induction theorem, Ekeland variational principle Category 1: Convex and Nonsmooth Optimization Citation: SIAM J. Optim., 2015, 25(4), 2561–2588. http://dx.doi.org/10.1137/140991157 Download: [PDF]Entry Submitted: 10/11/2014Entry Accepted: 10/11/2014Entry Last Modified: 12/18/2015Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.