- A remark on the lower semicontinuity assumption in the Ekeland variational principle Xuan Duc Ha Truong (txdhamath.ac.vn) Abstract: What happens to the conclusion of the Ekeland variational principle (briefly, EVP) if a considered function $f:X\to \R\cup\{+\infty\}$ is lower semicontinuous not on a whole metric space $X$ but only on its domain? We provide a straightforward proof showing that it still holds but only for $\epsilon$ varying in some interval $]0,\beta-\inf_Xf[$, where $\beta$ is a quantity expressing quantitatively the violation of the lower semicontinuity of $f$ outside its domain. This version of EVP collapses to the classical one when the function is lsc on the whole space. Keywords: Ekeland variational principle, lower semicontinuity, G\^ateaux differentiability Category 1: Nonlinear Optimization Citation: OPTIMIZATION, 2016 VOL. 65, NO. 10, 1781–1789 Download: Entry Submitted: 07/09/2015Entry Accepted: 07/09/2015Entry Last Modified: 04/24/2017Modify/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.