A local primal-dual interior-point method for optimizing the eigenvalues of hermitian definite pencils
We consider the following optimization problem; minimize the largest eigenvalue of a hermitian definite matrix pencil (A(x), B(x)), i.e. the largest root of det A(x)-{lambda}B(x) = 0, where A(x) is hermitian, B(x) is hermitian definite, and x is a vector of free parameters. This is a quasiconvex problem if the pencil depends affinely upon the parameters, reducing to semidifinite programming in the special case that B(x) is the identity matrix for all x. A new form of the optimality conditions is given, emphasizing a complementarity condition on primal and dual matrices. Newton`s method is then applied to these conditions to give a new locally quadratically convergent interior-point method which works well in practice.
- OSTI ID:
- 36101
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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