Secant relations versus positive definiteness in quasi-Newton methods

The effect of using a nonsymmetric and nonpositive-definite matrix for approximation of the Hessian inverse in unconstrained optimization is investigated. To this end, a new algorithm, which may be viewed as a member of the Huang family, is derived. The proposed algorithm possesses the quadratic termination property without exact line search. It seems from the numerical results that it is not essential to use a symmetric and positive-definite matrix.