Full Stability of Locally Optimal Solutions in Second-Order Cone Programs
Boris S. Mordukhovich, Jiří V. Outrata, M. Ebrahim Sarabi · SIAM Journal on Optimization · 2014
The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to second-order cone programs (SOCPs) expressed entirely in terms of their initial data. These characterizations are obtained via appropriate versions of the quadratic growth and strong second-order sufficient conditions under the corresponding constraint qualifications. We also establish close relationships between full stability of local minimizers for SOCPs and strong regularity of the associated generalized equations at nondegenerate points. Our approach is mainly based on advanced tools of second-order variational analysis and generalized differentiation.