- A version of the Ekeland variational principle for an extended real-valued function which is lower semicontinuous on its domain Xuan Duc Ha Truong(txdhamath.ac.vn) Abstract: The well-known Ekeland variational principle (in brief, EVP) concerns a function $f:X\to\R\cup\{+\infty\}$, which is lower semicontinuous (in brief, lsc) and bounded from below on a complete metric space $X$. In this note, we answer the question: What happens when the assumption $f$ is lsc on $X$" is relaxed to $f$ is lsc on its domain"? We show that, in such a situation, the conclusion of EVP holds for $\epsilon$ varying in some interval $]0,\gamma -\inf_Xf[$. Here, $\gamma$ is the supremum of scalars $t$ with $t>\inf_Xf$ such that lower level sets $[f\leq t]$ are closed and it also is calculated based on information about the behavior of $f$ at the boundary of its domain. When $f$ is lsc on the whole space $X$, our version of EVP reduces to the classical one with $\gamma =+\infty$. Keywords: Ekeland variational principle, lower semicontinuity, Gateaux differentiability Category 1: Nonlinear Optimization (Other ) Citation: Download: [PDF]Entry Submitted: 05/31/2015Entry Accepted: 05/31/2015Entry Last Modified: 05/31/2015Modify/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.