Piecewise Sequential Quadratic Programming For Mathematical Programs With . . .

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. KEY WORDS MPEC, bilevel program, nonlinear complementarity problem, nonlinear program, first- and second-order optimality conditions, linear independence constraint qualification, sequential quadratic programming, quadratic convergence. 2 Chapter 1 1 INTRODUC..