190. Random Newton-type Iterations with Application to Electronic Structure Determination
Invited abstract in session WE-5: Randomized optimization algorithms part 1/2, stream Randomized optimization algorithms.
Wednesday, 14:10 - 15:50Room: M:N
Authors (first author is the speaker)
| 1. | Titus Pinta
|
| Mathematics, ENSTA |
Abstract
We combine two separate theories in the context of molecular electronic structure determination. On the one hand, we present a general framework of Newton-type methods for root-finding problems, with constraints, that characterizes classes of functions for which superlinear or better convergence is guaranteed. On the other hand we present a theory of random function iterations, where the functions are randomly selected mappings generated from familiar optimization problems. Putting these two ideas together yields a Markov operator whose kernel is given by the Newton-type mapping of a random variable to the critical point set of a randomly generated optimization problem. The "fixed points" that we seek are invariant measures of the corresponding Markov operator. In the context of molecular electronic structure determination, the optimization problem is a maximum liklihood estimation problem. We present the foundations of both theoretical threads and preliminary results of their combination toward reconstructing molecular electronic structures from X-ray free electron laser measurements.
Keywords
- SS - Advances in Nonlinear Optimization and Applications
Status: accepted
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