INTERPOLATION BY CONIC MODEL FOR UNCONSTRAINED OPTIMIZATION

This paper describes a method for unconstrained optimization that asso ciates quasi-Newton methods with conic functions. The derivation is ba sed upon the construction of a conic function so that a local nonquadr atic model can interpolate two function and one gradient values of the objective function at the last two interates as a natural extension o f existing quasi-Newton methods. The new method is shown to have Q-sup erlinear rate of convergence under standard assumptions on the objecti ve function, and to decrease the number of line searches for good choi ce of parameters. Numerical experiments verify that the new method is very successful.