##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Linghao Zhang

#### UCSD

## Polynomial Optimization over Unions of Sets

##### Abstract:

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove the asymptotic or finite convergence of the unified hierarchy. Special properties for the univariate case are discussed. The numerical experiments demonstrate that solving this unified hierarchy takes less computational time than optimizing the objective over each individual constraining subset separately. The application for computing (p,q)-norms of matrices is also presented.

### February 27, 2024

### 11:00 AM

APM 2402 and Zoom ID 990 3560 4352

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