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Modified Line Search Strategy and Its Applications in the Newton Method

Zhong Wan, Xiaodong Zheng, Yunyun Fei, Songhai Deng


In this paper, a new inexact line search strategy is proposed, where a rough step length is firstly obtained by implementing the steps of backtracking in the Armijo line search, then it is improved by incorporating the features of the step length satisfying the approximate Wolfe condition. On the basis of the new line search, a modified Newton algorithm is developed to solve the unconstrained optimization problems. Under some suitable assumptions, the global convergence theory is established. Numerical experiments demonstrate that the new algorithm is effective, especially in comparison with the similar methods available in the literature.


descent algorithm, unconstrained optimization, inexact line search, global convergence.

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