##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Tingting Tang

#### San Diego State University and SDSU Imperial Valley

## Application of numerical algebraic geometry in parametric semidefinite programming

##### Abstract:

In this talk, we study the property of the solution of semidefinite programs with multi-dimensional perturbation variables using the Davidenko di erential equations. Under the assumptions of strict complementary and non-degeneracy, we aim to find the a priori unknown maximal convex permissible perturbation set where the semidefinite program has a unique optimum and the optimum is analytic. A sweeping euler numerical method is developed to approximate this a priori unknown perturbation set and solve the semidefinite program within this set. We prove local and global error bounds for this second-order sweeping Euler scheme and demonstrate results on several examples.

Host: Melvin Leok

### May 18, 2021

### 11:00 AM

### Zoom ID 939 3177 8552

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