Newton’s method for convex optimization

Abstract

In this chapter we deal with the convex optimization problem (COP). Using the generalized-Newton’s algorithm (GNA) we generate a sequence that converges to a solution of the COP. We use weak-center and weak Lipschitz-type conditions in our semilocal convergence analysis leading to a finer convergence analysis than in earlier studies. Numerical examples where earlier sufficient convergence conditions are not satisfied but our conditions are satisfied are also presented in this chapter.