Optimizing with respect to two variables (p and d)

[jason-hn]

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]

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 [email protected] 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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