##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Minxin Zhang

#### UCSD

## A Projected-Search Interior Method for Nonlinear Optimization

##### Abstract:

Projected-search methods for bound-constrained optimization are based on performing a search along a piecewise-linear continuous path obtained by projecting a search direction onto the feasible region. A potential benefit of a projected-search method is that the direction of the search path may change multiple times at the cost of computing a single direction.

In this talk, we present a new interior method for general nonlinearly constrained optimization that combines a shifted primal-dual interior method with a projected-search method for bound-constrained optimization. The method is based on the formulation of a primal-dual penalty-barrier function that incorporates shifts on both primal and dual variables. A modified Newton direction is used in conjunction with a new projected-search algorithm that employs a non-monotone flexible quasi-Armijo line search for the minimization of the penalty-barrier function. Computational results indicate that the proposed method requires fewer iterations than a conventional interior method, thereby reducing the number of times that the search direction need be computed.

### November 22, 2022

### 11:00 AM

APM 2402 and Zoom ID 986 1678 1113

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