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alecjacobson / computer-graphics-mass-spring-systems

Computer Graphics Assignment – Mass Spring Systems
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Optimizing with respect to two variables (p and d) #23

Open hanmingrui159 opened 4 years ago

hanmingrui159 commented 4 years ago

Hi, I am just a little confused why the two-steps work on a calculus-level:

First, is the output space of the expression convex? Otherwise, we might run into issues that more than one possible location at the next timestamp.

Second, how do we make sure that each time we minimize one of the two variables (LaTeX: d_{ij}d i j and LaTeX: p_ip i), the overall expression will get closer to any local min?

Thanks!

abhimadan commented 4 years ago

The time steps are relatively small, so it’s unlikely we’ll find a “bad” local minimum. The optimization algorithm we’re using is known as block coordinate descent, which is similar to gradient descent and should converge for nice functions like what we’re working with.

On Dec 6, 2019, at 1:12 AM, Mingrui Han notifications@github.com wrote:

 Hi, I am just a little confused why the two-steps work on a calculus-level:

First, is the output space of the expression convex? Otherwise, we might run into issues that more than one possible location at the next timestamp.

Second, how do we make sure that each time we minimize one of the two variables (LaTeX: d_{ij}d i j and LaTeX: p_ip i), the overall expression will get closer to any local min?

Thanks!

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