#

# SparseCoLO

# (Conversion Methods for SPARSE
COnic-form Linear
Optimization)

#### K. Fujisawa, S. Kim, M. Kojima, Y. Okamoto and M. Yamashita

#### February 12, 2008

#### Revised
April,
2010

####

#### SparseCoLO
is a Matlab package for implementing the four
conversion methods, proposed
by Kim, Kojima, Mevissen and Yamashita, via positive
semidefinite matrix completion for an optimization problem with matrix inequalities
satisfying **a sparse chordal graph structure**. It is based
on quite a general description of optimization problem including both
primal and dual form of linear, semidefinite, second-order
cone programs with equality/inequality constraints. Among the four conversion methods,
two methods utilize the domain-space sparsity of a semidefinite
matrix variable and the other two methods the range-space
sparsity of a linear matrix inequality (LMI) constraint
of the given problem. **SparseCoLO**
can be used as a preprocessor
to reduce the size of the given problem before applying semidefinite
programming solvers.

Paper: S. Kim, M.
Kojima, M. Mevissen, and M. Yamashita
, "Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix
completion," Research Report B-452, Dept. of Mathematical and Computing Sciences, Tokyo Institute
of Technology, Oh-Okayama, Meguro, Tokyo 152-8552, Japan.

**We are collecting
instances of sparse linear optimization problems (LOPs)
to evaluate and improve the performance of SparseCoLO.
Any instances of sparse LOPs that you could send
us to**

kojima.m.aa-sparsecolo ''insert at'' m.titech.ac.jp.

**would**** be very much appreciated**.

###

**
SparseCoLO is now distributed under the GNU GPL (General Public
License) v2.
**

**
**
If you have any question, please send a message to kojima.m.aa-sparsecolo ''insert at'' m.titech.ac.jp.