Generalized equations, variational inequalities and a weak Kantorovich theorem

作者：Uko Livinus U^*; Argyros Ioannis K

来源：Numerical Algorithms, 2009, 52(3): 321-333.

DOI：10.1007/s11075-009-9275-2

• Generalized equation
• Variational inequality
• Nonlinear complementarity problem
• Nonlinear operator equation
• Kantorovich theorem
• Generalized Newton's method
• Center-Lipschitz condition

We prove a Kantorovich-type theorem on the existence and uniqueness of the solution of a generalized equation of the form f (u) g(u) 0 where f is a Frechet-differentiable function and g is a maximal monotone operator defined on a Hilbert space. The depth and scope of this theorem is such that when we specialize it to nonlinear operator equations, variational inequalities and nonlinear complementarity problems we obtain novel results for these problems as well. Our approach to the solution of a generalized equation is iterative, and the solution is obtained as the limit of the solutions of partially linearized generalized Newton subproblems of the type Az g(z) (sic) b where A is a linear operator.

• 出版日期2009-11