##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Ren-Cang Li

#### University of Texas, Arlington

## A Krylov Subspace Method for Large-Scale Second-Order Cone Linear Complementarity Problem

##### Abstract:

Optimization problems with second order cone constraints have wide range of applications in engineering, control, and management science. In this talk, we present an efficient method based on Krylov subspace approximation for solving the second order cone linear complementarity problem (SOCLCP). Here, we first show that SOCLCP can be solved by finding a positive zero $s_*\in \mathbb{R}$ of a particular rational function $h(s)$, and then propose a Krylov subspace method to reduce $h(s)$ to $h_{\ell}(s)$ as in the model reduction. The zero $s_*$ of $h(s)$ can be accurately approximated by that of $h_{\ell}(s)=0$ which itself can be casted as a small eigenvalue problem. The new method is made possible by our complete description of the curve $h(s)$, and it is suitable for large scale problems. The new method is tested and compared against the bisection method recently proposed and two other state-of-the-art packages: SDPT3 and SeDuMi. Our numerical results show that the method is very efficient both for small-to-medium dense problems as well as for large scale problems. This is a joint work with Lei-Hong Zhang (Shanghai University of Finance and Economics), Wei Hong Yang (Fudan University), and Chungen Shen (Shanghai Finance University).

Host: Jiawang Nie

### November 24, 2015

### 2:00 PM

### AP&M 6402

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