Tilt stability of a local minimum

作     者：Poliquin, RA Rockafellar, RT 

作者机构：Univ Alberta Dept Math Sci Edmonton AB T6G 2G1 Canada Univ Washington Dept Math Seattle WA 98195 USA Univ Perpignan F-66025 Perpignan France 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 (工业与应用数学会最优化杂志)

年 卷 期：1998年第8卷第2期

页      面：287-299页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：variational analysis second-order optimality tilt stability perturbations sensitivity prox-regularity amenable functions generalized Hessians coderivatives monotone mappings 

摘      要：The behavior of a minimizing point when an objective function is tilted by adding a small linear term is studied from the perspective of second-order conditions for local optimality. The classical condition of a positive-definite Hessian in smooth problems without constraints is found to have an exact counterpart much more broadly in the positivity of a certain generalized Hessian mapping. This fully characterizes the case where tilt perturbations cause the minimizing point to shift in a Lipschitzian manner.