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Are the iterative steps in optimization affected by the intrinsic and extrinsic curvatures of the objective functions ? and How?

Is there any geometric and intuitive demo show illustrating the direction and modulus of such iterative steps as Newton-like methods and steepest descent and conjugate gradient methods?

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    $\begingroup$ This is a better question for Google than for MathOverflow. $\endgroup$
    – guest
    Commented Feb 10, 2014 at 1:01
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    $\begingroup$ thank you! Google and youtube sometimes don't work for me due to GFW $\endgroup$
    – LCFactorization
    Commented Feb 10, 2014 at 4:05

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Maybe these images will help?

     enter image description here
     
(Image by Ruye Wang at this link.)
     ZigZagging      
(Image at this link.)
If you prefer dynamic illustrations, there is this YouTube video:
     YouTubeGradient

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  • $\begingroup$ thank you very much! How do you obtain such impressive images? $\endgroup$
    – LCFactorization
    Commented Feb 10, 2014 at 4:02

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