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A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems. (English) Zbl 0733.90063
This paper presents a globally convergent, locally quadratically convergent algorithm for solving general nonlinear programs, nonlinear complementarity and variational inequality problems. The algorithm is based on a unified formulation of these three mathematical programming problems as a certain system of B-differentiable equations, and is a modification of the damped Newton method proposed by the author in another paper for solving such a system of nonsmooth equations. The algorithm resembles some existing methods to solve these classes of mathematical programs, but has its own features; in particular, it possesses the combined advantage of a fast quadratic rate of convergence of a basic Newton method and the desirable global convergence induced by one-dimensional Armijo line searches.
In the context of a nonlinear program, the algorithm is of the sequential quadratic programming type with two distinct characteristics: (1) it makes no use of a penalty function; (2) it circumvents the Maratos effect. In the context of the variational inequality/complementarity problem, the algorithm provides a Newton-type descent method that is guaranteed globally convergent without requiring the F-differentiability assumption of the defining B-differentiable equations.

MSC:
90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49J40 Variational inequalities
49J52 Nonsmooth analysis
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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References:
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