##### Department of Mathematics,

University of California San Diego

****************************

### Center for Computational Mathematics Seminar

## Alex Guldemond

#### UCSD

## A Shifted Primal-Dual Trust-Region Interior-Point Algorithm

##### Abstract:

Interior-point methods are some of the most effective and widely used methods to finding local minimizers of large-scale non-convex optimization problems. In this talk, we introduce three different mechanisms for ensuring global convergence to second-order local minimizers from arbitrary feasible starting points by solving a sequence of trust-region subproblems defined by quadratic models of a shifted primal-dual penalty-barrier merit function. Each of these methods begins by solving the trust-region subproblem to form a new trial point, and proceeds to refine the trial iterate until a sufficient-decrease condition is met. We suggest two different definitions of the trust region, and provide numerical results comparing each of the different approaches.

### March 8, 2022

### 11:00 AM

Zoom ID 922 9012 0877

****************************