A new linesearch method for quadratically constrained convex programming

A new method is proposed for the linesearch procedure in logarithmic barrier function and other interior point methods for convex quadratically constrained quadratic programming problems, which includes linear and quadratic programming as special cases. The method consists in transforming the derivative of the function obtained in this linesearch, so that Newton’s method for finding its unique root will be globally convergent. It is equally useful in solving a problem in a matrix theory, namely the computation of the eigenvalues of a matrix, perturbed by the addition of a matrix of rank one. An improved Newton method is also presented together with numerical results.