Second-order variational analysis in second-order cone programming

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 together with an error bound estimate in the general second-order cone programming setting involving twice differentiable data. On the other hand, we precisely calculate the graphical derivative of the normal cone mapping to Q under the 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. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.

Hang N.T.V.1, 2 , Mordukhovich B.S. 1, 3 , Sarabi M.E.4
  • 1 Department of Mathematics, Wayne State University, Detroit, MI 48202, United States
  • 2 Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, 10307, Viet Nam
  • 3 RUDN University, Moscow, 117198, Russian Federation
  • 4 Department of Mathematics, Miami University, Oxford, OH 45065, United States
Error bounds; Graphical derivative; Isolated calmness; Nonpolyhedral systems; Second-order conic programs; Second-order variational analysis; Twice epi-differentiability
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