##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Masakazu Kojima

#### Tokyo Institute of Technology

## Exploiting Structured Sparsity in Linear and Nonlinear Semidefiite Programs

##### Abstract:

This talk summarizes conversion of large scale linear and nonlinear SDPs, which satisfies the sparsity characterized by a chordal graph structure , into smaller scale SDPs. The sparsity is classified in two types, the domain-space sparsity (d-space sparsity) for the symmetric matrix variable in the objective and/or constraint functions of the SDP, which is required to be positive semidefinite, and the range-space sparsity (r-space sparsity) for a linear or nonlinear matrix-inequality constraint of the SDP. Some numerical results on the conversion methods indicate their potential for improving the efficiency of solving various problems.

Hosts: Philip Gill, Bill Helton and Jiawang Nie

### October 21, 2010

### 4:00 PM

### AP&M 6402

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