The non-monotone conic algorithm

In this paper we present a new algorithm for finding the unconstrained minimum of a continuously differentiate function f(x) in n variables. This algorithm is based on a conic model function, which does not involve the conjugacy matrix or the Hessian of the model function. The conic method in this paper is combined with a non-monotone line search. The method does not guarantee descent in the objective function at each iteration. The use of the stopping criterion introduced by Grippo, Lampariello and Lucidi allows the objective function to increase at some iterations and still guarantees global convergence.