##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Ziyan Zhu

#### UCSD

## Adaptive Cubic Regularization Methods for Nonconvex Unconstrained Optimization

##### Abstract:

Adaptive cubic regularization methods have several favorable properties for nonconvex optimization. In particular, under mild assumptions, they are globally convergent to a second-order stationary point. In this talk, I will introduce an adaptive cubic regularization method for unconstrained optimization. Methods analogous to those used to solve the trust-region subproblem will be discussed for solving the local cubic model. Some numerical results will be presented that compare a cubic regularized Newton's method, a standard trust-region method and a trust-search method.

### November 12, 2019

### 10:00 AM

### AP&M 2402

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