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A MODIFIED REGULARIZED NEWTON METHOD FOR UNCONSTRAINED NONCONVEX OPTIMIZATION

Heng Wang, Mei Qin, Haibo Wang

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Abstract

In this paper, we present a modified regularized Newton method for the unconstrained nonconvex optimization by using trust region technique. We show that if the gradient and Hessian of the objective function are Lipschitz continuous, then the modified regularized Newton method (M-RNM) has a global convergence property. Numerical results show that the algorithm is very efficient.

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What this paper is about

In this paper, we present a modified regularized Newton method for the unconstrained nonconvex optimization by using trust region technique. We show that if the gradient and Hessian of the objective function are Lipschitz continuous, then the modified regularized Newton method (M-RNM) has a global convergence property. Numerical results show that the algorithm is very efficient.

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Available abstract

In this paper, we present a modified regularized Newton method for the unconstrained nonconvex optimization by using trust region technique. We show that if the gradient and Hessian of the objective function are Lipschitz continuous, then the modified regularized Newton method (M-RNM) has a global convergence property. Numerical results show that the algorithm is very efficient.

Key concepts: Hessian matrix, Lipschitz continuity, Quasi-Newton method, Newton's method, Convergence (economics), Mathematics, Newton's method in optimization, Applied mathematics

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