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Van Ngai Huynh

Publications and source records attributed to Van Ngai Huynh.

5 recordsLinked to original sources
arXiv2026

Stochastic Model-Based Methods for Minimizing Paraconvex Functions

This paper studies stochastic algorithms for minimizing paraconvex functions, a function class that generalizes weakly convex functions and includes, for instance, Hölder smooth functions and compositions of convex functions with Hölder smooth maps. We first establish the convergence of the stochastic subgradient method and the stochastic proximal subgradient method for unconstrained and composite paraconvex optimization, respectively. The analysis is then extended to a broad family of algorithms that access the objective through stochastic models satisfying certain approximation-quality and continuity assumptions. The main principle that underlies the convergence analysis is that the algorithms under consideration can be interpreted as perturbed descent methods on the generalized Moreau envelope of the original paraconvex problem.

math.OC↗
arXiv2026

Finding directional stationary points of DC programs

We address the problem of computing stationary points for non-smooth, non-convex optimization problems. While this topic is well studied in the smooth setting, fewer algorithmic and theoretical results exist for the non-smooth case. Within Difference-of-Convex functions (DC) programming, the well-known DC Algorithm (DCA) is a standard method for computing critical points, whose definition depends on the chosen DC decomposition. More recently, some works have focused on computing directional stationary points - a stronger notion that does not depend on any particular DC decomposition - for specific non-smooth DC programs, where the second DC component is the pointwise maximum of finitely many smooth convex functions. In this contribution, we propose a new and unified approach for identifying directional stationary points of non-smooth DC programs, where both DC components may be non-smooth. Our framework generalizes both the classical DCA and the above recent approaches. It applies when the second DC component is the pointwise maximum of a continuous family of smooth convex functions, and more generally, to any continuous convex function on the whole space. We also establish strong convergence results. Specifically, when the second DC component is the pointwise maximum of finitely many $C^{1,1}$ - smooth convex functions, we prove under the Łojasiewicz inequality that the entire sequence generated by our algorithm converges. This extends previous results requiring global $C^{1,1}$ - smoothness. Finally, we introduce a randomized (stochastic) variant of our method and prove its almost sure convergence, thereby extending our deterministic results to the randomized setting.

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arXiv2015

Directional Hölder Metric Regularity

This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Hölder /Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Hölder /Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.

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arXiv2012

Metric regularity of composition set-valued mappings: metric setting and coderivative conditions

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years in the literature. In turn, these techniques are based on several important concepts (like error bounds, lower semicontinuous envelope of a set-valued map, local composition stability of multifunctions) and allow us to obtain two new proofs of a recent result having deep roots in the topic of regularity of mappings. Moreover, we make clear the idea that it is possible to use (co)derivative conditions as tools of proof for openness results in very general situations.

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