Optimality Conditions For MPEC Problems With Linear Second-order Cone Constraints

Second-order cone programming problems are a class of important optimization problems.Based on some prelimibaries in Nonsmooth Analysis and Set-valued Analysis. and the formulas about the limiting coderivative of the metric projection onto second-order cone,developed in[67],we derive optimality conditions for linear second-order cone MPEC problems under mild conditions.Sepecific optimality conditions for the linear second-order cone MPEC problem when the abstract constraint set is defined by NLP constraints,SDP constraints or second-order cone constraints,rsepectively.Especially,we obtain nonsmooth equation reformulation of optimality conditions when the constraint set is of the formΞ=R~m×9.