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 October 29th, 2014, 05:13 PM #1 Newbie   Joined: Oct 2014 From: Australia Posts: 1 Thanks: 0 Minimum for multivariable function using nonlinear Gauss Seidel Let $X_1$...$X_p$ spaces without specific property (i.e., non convex and it's no necessary subset of real numbers $\mathbb{R}$). Let a continuous function $f:X_1\times...\times X_p\rightarrow \mathbb{R}$ such that $f$ has a minimum point $X^*=(X_1^*,...,X_p^*)$ such that $$X_j^*=g_j(X_1^*,...,X_{j-1}^*,X_{j+1}^*,...,X_p^*),$$ where $g_j:X_1\times...\times X_{j-1}\times X_{j+1}\times...\times X_p\rightarrow X_{j}$ is continuous for all $j=1,...,p$. Now, I define a sequence $$X_j^{(k+1)}=g_j(X_1^{(k+1)},...,X_{j-1}^{(k+1)},X_{j+1}^k,...,X_p^k),$$ for all $k$. Let $X^k=(X_1^k,...,X_p^k)$. I could prove that sequence $\{f(X^{k})\}$ converge. Moreover, it is a decreasing sequence. But, Could I say $\{f(X^{k})\}$ converge to $\{f(X^*)\}$? Any answer will help me Tags function, gauss, gauss seidel, minimum, multivariable, nonlinear, seidel Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rayman Real Analysis 3 February 24th, 2013 08:17 AM dgemu Calculus 0 February 7th, 2011 11:15 AM wannabe1 Linear Algebra 2 February 2nd, 2010 09:56 PM chetanshreedhar Applied Math 0 April 6th, 2009 02:57 AM Schubatis1 Calculus 1 September 26th, 2008 08:13 PM

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