Mathematical Programming: Series A and B
First and second order analysis of nonlinear semidefinite programs
Mathematical Programming: Series A and B
Second Order Optimality Conditions Based on Parabolic Second Order Tangent Sets
SIAM Journal on Optimization
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In this article, we derive second-order necessary conditions of optimality for an abstract optimization problem with equality and inequality constraints and constraints in the form of an inclusion into a given closed set. An important feature is that our optimality conditions dispense with any a priori normality assumptions, such as Robinsons constraint qualification, and remain informative even for abnormal points. Moreover, our optimality conditions take into account the second-order effect of the curvature of the set in the inclusion constraints.