Second-order variational analysis in second-order cone programming

• 成果类型: Article
• 署名作者: Hang, Nguyen T. V.; Mordukhovich, Boris S.; Sarabi, M. Ebrahim
• 署名单位: Wayne State University; Vietnam Academy of Science & Technology (VAST); Peoples Friendship University of Russia; University System of Ohio; Miami University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1345-6
• 发表日期: 2020
• 页码: 75-116
• 关键词: constraint systems; aubin property; STABILITY; calmness; derivatives; computation

摘要

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 Qis 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.