Linesearchers in interior point methods and perturbed eigenvalues
A new method is proposed for the linesearch procedure in logarithmic barrier function methods for convex quadratically constrained quadratic programming problems (which includes linear and quadratic programming as special cases) and for minimization over the cone of positive semidefinite matrices. It is equally useful in solving a problem in matrix theory, namely the computation of the eigenvalues of a matrix, perturbed by the addition of a matrix of rank one. This has applications in the singular value decomposition of a matrix as well as in other areas such as signal processing. In the linesearch case, the problem consists of finding the first positive root of a singular equation, whereas in the eigenvalue problem, all the roots of a very similar equation have to be computed. The nature of this equation, prevents the efficient use of any of the usual root finding methods. Our method is based on a nonlinear transformation of variables, transforming the singular function appearing in the aforementioned equation into one for which Newton`s method converges globally. An improved Newton method is also presented together with numerical results.
- OSTI ID:
- 36278
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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