##### Department of Mathematics,

University of California San Diego

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### Math 278C - Optimization and Data Science

## Hongchao Zhang

#### Louisiana State University

## Golden ratio primal-dual algorithm with linesearch

##### Abstract:

Golden ratio primal-dual algorithm (GRPDA) is a new variant of the classical Arrow-Hurwicz method for solving structured convex-concave saddle point problem. In this talk, we present GRPDAs with adaptive linesearch, which potentially allows much larger stepsizes, and hence, could significantly accelerate the convergence speed. We show global iterate convergence as well as O($\frac{1}{N}$) ergodic convergence rate results, measured by the function value gap and constraint violations of an equivalent optimization problem. When one of the component functions is strongly convex, faster O($\frac{1}{N^2}$) ergodic convergence rate can be established. In addition, linear convergence can be established when subdifferential operators of the component functions are strongly metric subregular. Our preliminary numerical results show our algorithms perform much better than other state-of-art

comparison algorithms.

Host: Jiawang Nie

### March 9, 2022

### 3:00 PM

https://ucsd.zoom.us/j/94927846567

Meeting ID: 949 2784 6567

Password: 278CWN22

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