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Characterizations of Variational Convexity and Tilt Stability via Quadratic Bundles

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arxiv 2501.04629 v1 pith:ENRELI6N submitted 2025-01-08 math.OC

Pham Duy Khanh , Boris S. Mordukhovich , Vo Thanh Phat , Le Duc Viet This is my paper · ORCID
classification math.OC
keywords bundlescharacterizationsquadraticconvexitydifferentiabilityfunctionsgeneralizedstability
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abstract

In this paper, we establish characterizations of variational $s$-convexity and tilt stability for prox-regular functions in the absence of subdifferential continuity via quadratic bundles, a kind of primal-dual generalized second-order derivatives recently introduced by Rockafellar. Deriving such characterizations in the effective pointbased form requires a certain revision of quadratic bundles investigated below. Our device is based on the notion of generalized twice differentiability and its novel characterization via classical twice differentiability of the associated Moreau envelopes combined with various limiting procedures for functions and sets.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Second-Order Characterizations of Tilt Stability in Composite Optimization

    math.OC 2025-07 conditional novelty 8.0 of 10

    The paper proves no-gap pointbased second-order characterizations of tilt-stable local minimizers for composite optimization with convex parabolically regular functions, under metric subregularity constraint qualification.

  2. On the hardness of deterministic second-order optimization of functions with Lipschitz gradients

    math.OC 2026-07 accept novelty 7.0 of 10

    No deterministic zero-respecting second-order algorithm can compute Goldstein approximate second-order stationary points of C^{1,1} functions within finitely many oracle calls; general deterministic algorithms need at...

  3. Characterizations of Strong Variational Sufficiency in General Models of Composite Optimization

    math.OC 2025-07 conditional novelty 7.0 of 10

    For composite optimization problems, strong variational sufficiency is equivalent to a generalized strong second-order sufficient condition and to positive definiteness of a generalized augmented Lagrangian Hessian.

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