##### Department of Mathematics,

University of California San Diego

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### Math 278C: Optimization and Data Science

## Prof. Tingting Tang

#### San Diego State University

## On computing the nonlinearity interval and MAPs of SDPs

##### Abstract:

In this talk, I will talk about the parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function along a fixed direction and on a compact set. For the perturbation along a fixed direction, it is proven that the continuity of the optimal set mapping could fail on a nonlinearity interval and the set of points where this failure occurs is finite. A numerical method is developed to numerically compute the nonlinearity interval and generalize to perturbations on a compact set. For multi-variable perturbations, a maximal analytic perturbation set (MAPs) is defined on which the analyticity of the optimal mapping holds. Numerical examples are given to demonstrate the performance.

Host: Jiawang Nie

### March 6, 2024

### 3:00 PM

APM 7321

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