arXiv subjects

Nguyen Huy Chieu

Publications and source records attributed to Nguyen Huy Chieu.

5 recordsLinked to original sources

arXiv2026

Revisiting the Constant-Rank Constraint Qualification for Second-Order Cone Programs

The constant rank constraint qualification (CRCQ) for second-order cone programs, introduced by Andreani et al. in [Math. Program. 202 (2023), 473 - 513], shares some desirable properties with its classical nonlinear programming counterpart; specifically, it guarantees strong second-order necessary conditions for optimality, and is independent of the Robinson constraint qualification. However, unlike the classical version, this new CRCQ can fail in the linear case, and it is unclear whether CRCQ implies the metric subregularity constraint qualification (MSCQ). The aim of this paper is to examine the CRCQ for second-order cone programs in the linear setting. First, we show that the facial constant rank property, which is a key requirement for the validity of CRCQ, does not always hold in this context. Then, we derive a necessary and sufficient condition for a feasible point to satisfy this property. After that, we establish an easily verifiable characterization of CRCQ. Finally, utilizing this characterization, we prove that CRCQ and MSCQ are equivalent.

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arXiv2025

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 removing the linear independence condition of gradients of equality constraint functions. Examples are provided illustrating our findings.

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arXiv2021

Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions

This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as the sum of a function twice differentiable in the extended sense and a subdifferentially continuous, prox-regular, twice epi-differentiable function. For such a function, which is not necessarily prox-regular, it is shown that the quadratic growth, the strong metric subregularity of the subdifferential at a local minimizer, and the positive definiteness of the subgradient graphical derivative at a stationary point are equivalent. In addition, other characterizations of the quadratic growth and the strong metric subregularity of the subdifferential are also given. Besides, properties of functions twice differentiable in the extended sense are examined.

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arXiv2019

Second order optimality conditions for strong local minimizers via subgradient graphical derivative

This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We prove that the positive definiteness of the subgradient graphical derivative of an extended-real-valued lower semicontinuous proper function at a proximal stationary point is sufficient for the quadratic growth condition. It is also a necessary condition for the latter property when the function is either subdifferentially continuous, prox-regular, twice epi-differentiable or variationally convex. By applying our results to the $\mathcal{C}^2$-cone reducible constrained programs, we establish no-gap second order optimality conditions for (strong) local minimizers under the metric subregularity constraint qualification. These results extend the classical second order optimality conditions by surpassing the well-known Robinson's constraint qualification. Our approach also highlights the interconnection between the strong metric subregularity of subdifferential and quadratic growth condition in optimization problems.

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arXiv2017

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 conditions for tilt stability. In particular, we show that each stationary point of a nonlinear programming problem satisfying the metric subregularity constraint qualification is a tilt-stable local minimizer if the classical strong second-order sufficient condition holds.

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