From c4375c26458285bdfef7e466154ebd86d132f7a3 Mon Sep 17 00:00:00 2001 From: Peter FRANEK Date: Tue, 14 Feb 2017 14:43:30 +0100 Subject: [PATCH] title change, small corrections --- main.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/main.tex b/main.tex index ee2a3dd..d5513c9 100755 --- a/main.tex +++ b/main.tex @@ -171,7 +171,7 @@ grestore % \begin{document} -\title{Solving Equations with Inherent Uncertainty\thanks{The research +\title{Solving Equations and Optimization Problems with Uncertainty\thanks{The research leading to these results has received funding from Austrian Science Fund (FWF): M 1980 and from the Czech Science Foundation (GACR) grant number 15-14484S with institutional support RVO:67985807.} } @@ -748,7 +748,7 @@ If we include, in the coboundary matrix, only columns corresponding to $(n-1)$-s order the rows ($n$-simplices) by the $u$-filtration, and then perform a column matrix reduction such that, after the reduction, the lowest nonzero element in each column is the last nonzero element in that row, then the desired $\beta$ is the filtration value corresponding to the row of the lowest nonzero element on the right hand side after the reduction.}, -we compute the smallest $\beta$ such that $f'|_{A_{r}\cap u_\beta}$ is not extendable: by Section~\ref{sec:algorithm-oracle} +we compute the largest $\beta$ such that $f'|_{A_{r}\cap u_\beta}$ is not extendable: by Section~\ref{sec:algorithm-oracle} the robustness of zero of $f$ on $u_{\beta}$ is at least $r-\alpha>0$ and \begin{equation*} \beta \leq \inf_{\|g-f\|\leq r-\alpha} \,\,\max_{x\in g^{-1}(0)} u(x)\leq \max_{x\in f^{-1}(0)} \, u(x). -- 2.22.0