Extension of quasi-Newton methods to mathematical programs with complementarity constraints. (English) Zbl 1038.90100

Summary: Quasi-Newton methods in conjunction with the piecewise sequential quadratic programming are investigated for solving mathematical programming with equilibrium constraints, in particular for problems with complementarity constraints. Local convergence as well as superlinear convergence of these quasi-Newton methods can be established under suitable assumptions. In particular, several well-known quasi-Newton methods such as BFGS and DFP are proved to exhibit the local and superlinear convergence.


90C52 Methods of reduced gradient type
65K10 Numerical optimization and variational techniques
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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