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Variational Analysis In Second-Order Cone Programming And Applications, Hang Thi Van Nguyen

Wayne State University Dissertations

This dissertation conducts a second-order variational analysis for an important class on nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone. These second-order cone programs (SOCPs) are mathematically challenging due to the nonpolyhedrality of the underlying second-order cone while being important for various applications. The two main devices in our study are second epi-derivative and graphical derivative of the normal cone mapping which are proved to accumulate vital second-order information of functions/constraint systems under investigation. Our main contribution is threefold:

- proving the twice epi-differentiability of the indicator function of the second-order cone and of the augmented Lagrangian associated with …