Complete Characterizations of Tilt Stability in Nonlinear Programming under Weakest Qualification Conditions

Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification

This paper investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus rules for subgradient graphical derivative, we obtain some pointbased characterizations of tilt-stable local minimizers along with an explicit formula for calculating the exact bound of tilt stability. These results extend the corresponding ones of H. Gfrerer and B.S.Mordukhovich [SIAM J. Optim. 25 (2015), 2081-2119] by relaxing the constraint qualification and…

Characterization of tilt stability via subgradient graphical derivative with applications to nonlinear programming

This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of unconstrained optimization problems in terms of a uniform positive definiteness of the subgradient graphical derivative of the objective function around the point in question. By applying this result to nonlinear programming under the metric subregularity constraint qualification, we derive a second-order characterization and several new sufficient conditio…

混合约束最优控制问题的一种新约束条件

A New Constraint Qualification for Mixed Constrained Optimal Control

本文提出一种新约束条件，用于解决混合约束最优控制问题中的渐近最优性条件，证明了渐近弱极值原理在满足新约束条件时等价于经典弱极值原理，并给出了该约束条件的有效性充分条件。

基于渐近KKT条件的连续时间非线性规划的新约束规格

A New Constraint Qualification for Continuous-Time Nonlinear Programming Based on Asymptotic KKT Conditions

提出一种新的约束规格AKKT-正则性，使得局部最优解满足KKT条件，并证明该规格是最弱的。

Characterizations of Tilt-Stable Minimizers in Second-Order Cone Programming

This paper is devoted to the study of tilt stability of local minimizers, which plays an important role in both theoretical and numerical aspects of optimization. This notion has been comprehensively investigated in the unconstrained framework as well as for problems of nonlinear programming with $C^2$-smooth data. Available results for nonpolyhedral conic programs were obtained only under strong constraint nondegeneracy assumptions. Here we develop an approach of second-order variational analysis, which allows us to establish complete neighborhood and pointbased characterizations of tilt stab…

Second-order subdifferential calculus with applications to tilt stability in optimization

The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of frst-order subdifferential mappings. We develop an extended second-order subdifferential calculus and analyze the basic second-order qualification condition ensuring the fulfillment of the principal seco…