An Extended CG-Method with a New Non-Monotone Line Search Procedure for Constrained Optimization

In this paper, a new type of non-quadratic models is proposed which based on non-quadratic conic model. The new model is based upon a non-linear scaling of a quadratic form and it employs a new line search technique which is suitable for non-convex optimization problems. A restarting procedure due to Powell, and based upon some earlier work of Beale, is implemented in this work. The new proposed method is derived and tested on several standard constraint test functions with promising numerical results.