For unconstrained optimization, Newton-type methods have good convergence properties, and areused in practice. The Newton’s method combined with a trust-region method (the TR-Newtonmethod), the cubic regularization of Newton’s method and the regularized Newton method withline search methods are such Newton-type methods. The TR-Newton method and the cubic regu-larization of N...

This paper presents a parameterized Newton method using generalized Jacobians and a Broyden-like method for solving nonsmooth equations. The former ensures that the method is well-deened even when the generalized Jacobian is singular. The latter is constructed by using an approximation function which can be formed for nonsmooth equations arising from partial diierential equations and nonlinear ...

Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...

‎in this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎the proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the newton equation system‎, ‎by using an inexact newton direction‎. ‎furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

A nonmonotone strategy for solving nonlinear systems of equations is introduced. The idea consists of combining eecient local methods with an algorithm that reduces monotonically the squared norm of the system in a proper way. The local methods used are Newton's method and two quasi-Newton algorithms. Global iterations are based on recently introduced box-constrained minimization algorithms. We...