A Modified Newton’s Method for Unconstrained Minimization
Copyright policy )A Modified Newton’s Method for Unconstrained Minimization
Newton’s method for the minimization of a function of several variables presents difficulties in the case where the Hessian matrix is not positive definite. Various modifications are known. Any such modification uses a factorization of the Hessian. This paper suggests using the symmetric decomposition established in an earlier paper by the same authors [7]. The direction of descent is then chosen in a natural and simple manner. The resulting algorithm competes well with other variations. Numerical results are also included.
Numerical optimization and variational techniques, Factorization of the Hessian, Other matrix algorithms, Minimization of a Function, Modifications, Newton's Method, Symmetric Decomposition, Factorization of matrices, Numerical Results, Algorithm
Numerical optimization and variational techniques, Factorization of the Hessian, Other matrix algorithms, Minimization of a Function, Modifications, Newton's Method, Symmetric Decomposition, Factorization of matrices, Numerical Results, Algorithm
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