##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Michael Ferry

#### UCSD

## Minimization: One Dimension at a Time

##### Abstract:

This talk will cover one of the more popular methods for unconstrained minimization and explore techniques to improve upon it. In particular, I will cover the BFGS method, a type of quasi-Newton method, where one seeks the minimizer by using a sequence of approximate quadratic models. The most important technique to improve upon this method is developed from the following idea, which is the heart of the talk: can we minimize a function over a k-dimensional subspace in such a way as to make minimizing over k+1 dimensions a trivial task? For quadratic functions, the answer turns out to be 'yes', which in turn motivates similar techniques for the nonlinear case. Some benefits are: we operate with significantly smaller matrices, have a smaller memory footprint, and can reinitialize the curvature at each iteration at little to no cost, which dramatically improves convergence when the function is ill-conditioned near the solution. Some knowledge of linear algebra will be helpful but not necessary - I will aim to make the talk as accessible as possible.

### October 9, 2008

### 11:00 AM

### AP&M B412

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