##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Minxin Zhang

#### UCSD

## A Piecewise Differentiable Line Search for Projected Search Optimization Methods

##### Abstract:

Line search methods for unconstrained optimization based on satisfying the Wolfe conditions impose a restriction on the value of the directional derivative of the objective function at the new iterate. Projected search methods for bound-constrained optimization involve a line search along a continuous piecewise-linear path, which makes it impossible to apply the conventional Wolfe conditions. We propose a new quasi-Wolfe line search for piecewise differentiable functions. The behavior of the line search is similar to that of a conventional Wolfe line search, except that a step is accepted under a wider range of conditions. These conditions take into consideration steps at which the line search function is not differentiable. Some basic results associated with a conventional Wolfe line search are established for the quasi-Wolfe case. After identifying the practical considerations needed for converting a Wolfe line search into a quasi-Wolfe line search, details of the imp lementation along with some numerical results will be presented.

### October 15, 2019

### 11:00 AM

### AP&M 2402

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