Convergence of the solution method for variational inequalities
We study the properties of the method proposed in literature for solving variational inequalities and its modifications. Linear convergence in the neighborhood of the solution is established for problems that satisfy second-order sufficient conditions. The problem of finding the solution x{sub *} of the variational inequality (F(x{sub *}), x-x{sub *}) {ge} 0, {forall} x {element_of} {Omega} = (x{element_of}R{sup n}{vert_bar} f{sub i}(x){le}O, i=1,...,l) has been studied by many authors. The numerical methods considered by them, despite their theoretically fast rate of convergence, usually converge only locally and are computationally highly complex, because each iteration solves auxiliary subproblems on the original nonlinear set {Omega}. In other methods, on the other hand, each iteration is efficiently executed and converges nonlocally to the solution, but we do not have the rate of convergence bounds which are typical for mathematical programming methods of the corresponding order.
- OSTI ID:
- 441176
- Journal Information:
- Cybernetics and Systems Analysis, Journal Name: Cybernetics and Systems Analysis Journal Issue: 3 Vol. 30; ISSN CYASEC; ISSN 1060-0396
- Country of Publication:
- United States
- Language:
- English
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