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Determinant maximization with linear matrix inequality
constraints

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Lieven Vandenberghe, Stephen Boyd, Shao-Po Wu

The problem of maximizing the determinant of a matrix subject to
linear matrix inequalities arises in many fields, including
computational geometry, statistics, system identification, experiment
design, and information and communication theory. It can also
be considered as a generalization of the semidefinite programming
problem.
We give an overview of the applications of the determinant maximization
problem, pointing out simple cases where specialized algorithms or
analytical solutions are known.We then describe an interior-point method,
with a simplified nalysis of the worst-case complexity and numerical
results that indicate that the method is very efficient, both in theory
and in practice.
Compared to existing specialized algorithms (where they are
available), the interior-point method will generally be slower;
the advantage is that it handles a much wider variety of problems.
Technical Report,
Information Systems Laboratory, Stanford University.
Submitted to SIMAX, March 1996.

Contact: vandenbe@isl.stanford.edu