From 14ffecbfed7a85797e584c47877ba75bc8d9ab6c Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sat, 1 Jun 2019 15:22:38 -0400 Subject: [PATCH] removed shortcut notation in trust-region formula --- doc/trustregion.lyx | 6 +++--- doc/trustregion.pdf | Bin 60124 -> 59984 bytes 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/doc/trustregion.lyx b/doc/trustregion.lyx index 3296da512..97bc6ec74 100644 --- a/doc/trustregion.lyx +++ b/doc/trustregion.lyx @@ -620,9 +620,9 @@ To find the intersection of the line between \begin{align*} \Delta & =\norm{\left(1-\tau\right)\delta x_{u}+\tau\delta x_{n}}\\ \Delta^{2} & =\left(1-\tau\right)^{2}\delta x_{u}^{\t}\delta x_{u}+2\tau\left(1-\tau\right)\delta x_{u}^{\t}\delta x_{n}+\tau^{2}\delta x_{n}^{\t}\delta x_{n}\\ -0 & =uu-2\tau uu+\tau^{2}uu+2\tau un-2\tau^{2}un+\tau^{2}nn-\Delta^{2}\\ -0 & =\left(uu-2un+nn\right)\tau^{2}+\left(2un-2uu\right)\tau-\Delta^{2}+uu\\ -\tau & =\frac{-\left(2un-2uu\right)\pm\sqrt{\left(2un-2uu\right)^{2}-4\left(uu-2un+nn\right)\left(uu-\Delta^{2}\right)}}{2\left(uu-un+nn\right)} +0 & =\delta x_{u}^{\t}\delta x_{u}-2\tau\delta x_{u}^{\t}\delta x_{u}+\tau^{2}\delta x_{u}^{\t}\delta x_{u}+2\tau\delta x_{u}^{\t}\delta x_{n}-2\tau^{2}\delta x_{u}^{\t}\delta x_{n}+\tau^{2}\delta x_{n}^{\t}\delta x_{n}-\Delta^{2}\\ +0 & =\left(\delta x_{u}^{\t}\delta x_{u}-2\delta x_{u}^{\t}\delta x_{n}+\delta x_{n}^{\t}\delta x_{n}\right)\tau^{2}+\left(2\delta x_{u}^{\t}\delta x_{n}-2\delta x_{u}^{\t}\delta x_{u}\right)\tau-\Delta^{2}+\delta x_{u}^{\t}\delta x_{u}\\ +\tau & =\frac{-\left(2\delta x_{u}^{\t}\delta x_{n}-2\delta x_{u}^{\t}\delta x_{u}\right)\pm\sqrt{\left(2\delta x_{u}^{\t}\delta x_{n}-2\delta x_{u}^{\t}\delta x_{u}\right)^{2}-4\left(\delta x_{u}^{\t}\delta x_{u}-2\delta x_{u}^{\t}\delta x_{n}+\delta x_{n}^{\t}\delta x_{n}\right)\left(\delta x_{u}^{\t}\delta x_{u}-\Delta^{2}\right)}}{2\left(\delta x_{u}^{\t}\delta x_{u}-\delta x_{u}^{\t}\delta x_{n}+\delta x_{n}^{\t}\delta x_{n}\right)} \end{align*} \end_inset diff --git a/doc/trustregion.pdf b/doc/trustregion.pdf index 0a733a059b4c7784c40c183d4d9cd87a4b9e1ccc..22dcac035f71186de65c374c7acd7b7f22c8c4a4 100644 GIT binary patch delta 19401 zcmY(qQ)4Dv6QcG9tJ+qUhF?I*Tv+qP}HW83C_=bMw+KVcozRX1vFt$@xigVr;` z16UZjIQaQtoL!vEjBH^%Hjj05;62QE&RF(fDku$)TTYN9p1$M^iBP{`#S?}8O2#X`VM1Q|-lbjc zWf5A%i)EM&Jj)SDC6fwKS|yL~c|BfU0Q_`VM^^0D0Fd1L^9!`ZXrsc3?o0_9e`M72 z;Buf$lgaSTCGjGNNbdxSx3EAg23ZTO3_qtZMiY!zY+-%ktGY^iyI`z3EB_f6eX>7a z*S4?B*=lTA4c4yG-J-h|{8CoY!05q04cwm8ubPajsrg(KRw+6(cJAOD$TiqS0=n__ zM@m9@BbYS>0*))uFH(?OH`lC7@mchYfD;CF~wJ|v*ijI0NSj)(=5UbL25}+TDpwb;UZeLo_tD#$d7;UcM3JO zdm_$^3YVSNPf11Kka91k_~?$x|g^YXlp_2)POUQm&d$gT=>Ov|ZqCzgKBbA+DjC znk9=eNzenMuvl#CYh#bN07O5t2zqV$awdsMvEwNBXhCaWilWkG7qDo(fDRE$1#my! z^QSdlT+cPZqted?xEaAn34}xkK_(sWilxxy@Pesi3$%AOF>uT>n{I7jfve3}Lsw|V>I_H%7?j_y0 zs4!N&WU{i@SI>5tKOzWcn)e>`F>q{oBAcZ;7qgv`Aa#e-2TFwsG|}h232PdW;sB!% 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