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steepest descent, optimal step size, 76 iterations |
steepest descent, fixed step size \(h=0.25\), 150 iterations |
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The objective function is \(f(u) = (11-u_1-u_2)^2 + (1+u_1+10 u_2-u_1 u_2)^2\)
Starting from \(u^0=\{14;23.59\}\).
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steepest descent, optimal step size, 76 iterations |
steepest descent, fixed step size \(h=0.25\), 150 iterations |
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THe search using optimal step size is slower (due to performing line search at each step) and consumes more CPU time, but it does converge. While the search using fixed step is faster (since it does not perform line search) but it failed to converge when it \(u^k\) was very close to \(u^\ast \) due to oscillation around \(u^\ast \) as the step size was relatively large.
