2017/07/24 by Hang, Nguyen T. V., Mordukhovich, Boris S., Sarabi, M. Ebrahim
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1707.07766
The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone Q. From one hand, we prove that the indicator function of Q is always twice epi-differentiable and apply this result to characterizing the uniqueness of Lagrange multipliers at stationary points together with an error bound estimate in the general second-order cone setting involving \cal C2-smooth data. On the other hand, we precisely calculate the graphical derivative of the normal cone mapping to Q under the weakest metric subregularity constraint qualification and then give an application of the latter result to a complete characterization of isolated calmness for perturbed variational systems associated with second-order cone programs. The obtained results seem to be the first in the literature in these directions for nonpolyhedral problems without imposing any nondegeneracy assumptions.