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Piecewise sequential quadratic programming for mathematical programs with nonlinear complementarity constraints. (English) Zbl 0897.90184

Migdalas, Athanasios (ed.) et al., Multilevel optimization: algorithms and applications. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 20, 209-229 (1998).
Summary: We describe some first- and second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Mathematical programs with parametric nonlinear complementarity constraints are the focus. Of interest is the result that under a linear independence assumption that is standard in nonlinear programming, the otherwise combinatorial problem of checking whether a point is stationary for an MPEC is reduced to checking stationarity of single nonlinear program. We also present a piecewise sequential quadratic programming (PSQP) algorithm for solving MPEC. Local quadratic convergence is shown under the linear independence assumption and a second-order sufficient condition. Some computational results are given.
For the entire collection see [Zbl 0881.00028].

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C31 Sensitivity, stability, parametric optimization
90C20 Quadratic programming
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