Abstract
Consider a generalized equation problem: Find a point z is an element of R-n such that
0 is an element of F(z) + T(z),
where F : R-n -> R-n is a semismooth mapping and T : R-n paired right arrows R-n is a set-valued and maximal monotone operator. We construct a nonsmooth version of Newton's method to solve the generalized equation. The local convergence result of sequences generated by Newton's method is established. In particular, applications to variational inequality problems are provided.
| Original language | American English |
|---|---|
| Pages (from-to) | 865-878 |
| Journal | Journal of Nonlinear and Convex Analysis |
| Volume | 17 |
| Issue number | 5 |
| State | Published - 2016 |
Keywords
- BANACH-SPACE
- EQUATIONS
- NONLINEAR COMPLEMENTARITY-PROBLEMS
- Newton's method
- OPERATORS
- Set-valued mapping
- UNIQUENESS
- VARIATIONAL INEQUALITY
- generalized equation
- semismoothness