Author(s)

Huicheng Liu ¹, Han Zhang ²

Affiliation(s)

¹ School of Insurance, Guangdong University of Finance, Guangzhou, 510521, Guangdong, China
² School of Business Administration, Guangdong University of Finance, Guangzhou, 510521, Guangdong, China

Corresponding Author

Han Zhang

ABSTRACT

After a series of changes, many application problems in the fields of transportation, finance, economy, engineering technology and resource allocation are equivalent to solve a class of nonsmooth operator equations. In order to solve the nonsmooth operator equations and study its application in Banach space, this paper develops a semismooth Newton method and inexact-Newton method via a generalized inverse. The global, local and superlinear convergence of a semismooth Newton method are shown, the superlinear and linear convergence properties of an inexact Newton method are also proved. The present methods can be easier to perform than the previous ones in some applications, and viewed as the extensions of existing methods to solve nonsmooth operator equations.

KEYWORDS

Nonsmooth Operator Equations, Semismooth Newton Method, Inexact-Newton Method, Superlinear Convergence, Bounded Outer Inverse

CITE THIS PAPER

Huicheng Liu, Han Zhang, A Semismooth and an Inexact Newton Method for Solving Nonsmooth Operator Equations. Transactions on Computational and Applied Mathematics (2022) Vol. 2: 1-7. DOI: http://dx.doi.org/10.23977/tracam.2022.020101.

REFERENCES

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[9] Milzarek, A., Xiao, X., Cen, S., Wen, Z. and Ulbrich,M. (2019) A Stochastic Semismooth Newton Method for Nonsmooth Nonconvex Optimization. SIAM Journal on Optimization, 29,1-40. 
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