An efficient descent direction method with cutting planes

In this paper, a new hybrid method is proposed which combines the advantages of descent methods and cutting plane approaches. The new method gets fast to near-optimal region by using cutting planes and preserves the good convergence properties of descent methods near the optimum. The method is tested on convex functions, least squares problems and on parameter estimation by comparing its performance to well-known methods. Numerical experiments show that the proposed method is very efficient on all the examined problem types and performs in average much better than the benchmark methods.