convex optimization: provably easy, but non-trivial

Andy Casey and I discovered bad convergence issues and bad optimization problems in our multi-abundance Cannon model. This got me discouraged: It is a convex optimization, how hard can it be? At the end of the day, we quickly coded up analytic derivatives for the model and are hoping that these will fix our optimization problems (and vastly speed up optimization). In theory, analytic derivatives in our 17-label model should speed up our code by a factor of around 170, since the quadratic model has a lot of parameters!

At group meeting, Adrian Price-Whelan talked about chaotic models for the Ophiuchus Stream, Chang Hoon Hahn (NYU) talked about fiber collisions (our top-favorite subject at group meeting!), and Robyn Sanderson talked about the mutual information between chemical abundances and dynamical actions. In the fiber-collision discussion, we veered into the usual talk about solving all of astronomy: If we have a generative model for everything, we can deal with fiber collisions. That's not practical, but it got us talking about what a forward-modeling approach to large-scale structure might look like. I amused Blanton with the point that not any function you write down can consistently be thought of as a spatial correlation function: There are positive-definiteness requirements.

In the afternoon at Simons, there was a talk by Patrick Combettes (Paris 6) about convex optimization problems from a math perspective. He made connections—which we have been making here—between set intersection and optimization, which were interesting. He was very negative on non-convex optimization, in the sense that he doesn't think that there is much that can be said or proven about such problems, even fairly simple ones like bilinear.

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