NonlinOptTheory - Revision history

Rb: /* Iteration increments */

2015-04-14T11:50:11Z

‎Iteration increments

2015-04-14T11:49:17Z

‎Iteration increments

2015-04-14T11:48:13Z

‎Iteration increments

2015-04-14T11:47:49Z

‎Iteration increments

2015-04-14T11:47:27Z

‎Iteration increments

2015-04-14T11:47:05Z

‎Iteration increments

2015-04-14T11:46:29Z

‎Iteration increments

2015-04-14T11:45:41Z

‎Iteration increments

2015-04-14T11:45:26Z

‎Iteration increments

2015-04-14T11:44:51Z

‎Iteration increments

@@ Line 90: / Line 90: @@
 <math>\begin{aligned}
 \theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-\left( \left. \frac{\partial ^{2}S\left( \theta \right) }{\partial \theta \partial \theta'}\right\vert_{\theta =\widehat{\theta }^{\left( 0\right) }}\right) ^{-1}\left. \frac{\partial S\left( \theta \right) }{\partial \theta }\right\vert _{\theta =\widehat{\theta }^{\left( 0\right) }} \notag \\
-\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta}^{(0)} \right) G\left( \widehat{\theta }^{\left(
+\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta}^{(0)} \right) G\left( \widehat{\theta }^{\left( 0\right) }\right) \\
-\right) }\right)
+(k \times 1) &=& (k \times 1) - (k \times k) (k \times 1)
 \end{aligned}
 </math>

@@ Line 90: / Line 90: @@
 <math>\begin{aligned}
 \theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-\left( \left. \frac{\partial ^{2}S\left( \theta \right) }{\partial \theta \partial \theta'}\right\vert_{\theta =\widehat{\theta }^{\left( 0\right) }}\right) ^{-1}\left. \frac{\partial S\left( \theta \right) }{\partial \theta }\right\vert _{\theta =\widehat{\theta }^{\left( 0\right) }} \notag \\
-\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta}^{(0)} \right)
+\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta}^{(0)} \right) G\left( \widehat{\theta }^{\left(
 \end{aligned}
 </math>

@@ Line 90: / Line 90: @@
 <math>\begin{aligned}
 \theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-\left( \left. \frac{\partial ^{2}S\left( \theta \right) }{\partial \theta \partial \theta'}\right\vert_{\theta =\widehat{\theta }^{\left( 0\right) }}\right) ^{-1}\left. \frac{\partial S\left( \theta \right) }{\partial \theta }\right\vert _{\theta =\widehat{\theta }^{\left( 0\right) }} \notag \\
-\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta}^{99} \right)
+\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta}^{(0)} \right)
 \end{aligned}
 </math>

@@ Line 90: / Line 90: @@
 <math>\begin{aligned}
 \theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-\left( \left. \frac{\partial ^{2}S\left( \theta \right) }{\partial \theta \partial \theta'}\right\vert_{\theta =\widehat{\theta }^{\left( 0\right) }}\right) ^{-1}\left. \frac{\partial S\left( \theta \right) }{\partial \theta }\right\vert _{\theta =\widehat{\theta }^{\left( 0\right) }} \notag \\
-\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta} \right)
+\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta}^{99} \right)
 \end{aligned}
 </math>

@@ Line 90: / Line 90: @@
 <math>\begin{aligned}
 \theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-\left( \left. \frac{\partial ^{2}S\left( \theta \right) }{\partial \theta \partial \theta'}\right\vert_{\theta =\widehat{\theta }^{\left( 0\right) }}\right) ^{-1}\left. \frac{\partial S\left( \theta \right) }{\partial \theta }\right\vert _{\theta =\widehat{\theta }^{\left( 0\right) }} \notag \\
-\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \theta \right)
+\theta _{0} &=&\widehat{\theta }^{\left( 0\right) }-H^{-1} \left( \widehat{\theta} \right)
 \end{aligned}
 </math>

@@ Line 79: / Line 79: @@
 \partial \theta }\right\vert _{\theta =\widehat{\theta }^{\left( 0\right)
 }}+ \left. \frac{\partial ^{2}S\left( \theta \right) }{\partial \theta \partial \theta'}\right\vert
-_{\theta =\widehat{\theta }^{\left( 0\right) }}\left( \theta _{0}-\widehat{\theta }^{0}\right)  \label{Taylor}</math>
+_{\theta =\widehat{\theta }^{\left( 0\right) }}\left( \theta _{0}-\widehat{\theta }\right)  \label{Taylor}</math>
 As noted earlier, at the minimum: