Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints

[2606.28965] Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2606.28965 (math) [Submitted on 27 Jun 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints Authors: N. X. D. Bao , Tan H. Cao View a PDF of the paper titled Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints, by N. X. D. Bao and Tan H. Cao View PDF HTML (experimental) Abstract: We develop a second-order sensitivity theory for the efficient solution map \(S\) of a parametric vector optimization problem \(\min_C f(p,x)\) subject to \(x\in H(p)\). The main point is the passage from efficient values to efficient decisions. Under a value-to-decision error bound (VDB), second-order information for the marginal map \(\Phi\) lifts to a second-order Dini formula for \(S\). We first work in the abstract inclusion model \(x\in H(p)\), where outer and inner estimates yield second-order semi-derivability of \(S\). We then specialize to structured feasible maps \(H(p)=\{x\in\Omega:g(p,x)\in D\}\). Under Robinson metric regularity along \(\Omega\), second-order regularity of \(\Omega\) and \(D\), and directional second-order semi-derivability of the data, we obtain explicit formulas for \(\DD H\), \(\DD\Phi\), and \(\DD S\). The framework is specialized to polyhedral inequality/equality systems and illustrated by a robust multi-objective portfolio model and a DC-dispatch model for electricity markets, with a brief discussion of complementarity-based extensions. Comments: Keywords: parametric vector optimization; efficient solution map; marginal map; second-order Dini derivative; set-valued directional derivative; Robinson metric regularity; value-to-decision error bound; uniform Henig efficiency; parametric constraint system Subjects: Optimization and Control (math.OC) MSC classes: 49J53, 49K40, 90C29, 90C31, 90C46 Cite as: arXiv:2606.28965 [math.OC] (or arXiv:2606.28965v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2606.28965 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Bao X. D. Nguyen PhD [ view email ] [v1] Sat, 27 Jun 2026 15:05:06 UTC (38 KB) [v2] Sat, 15 Aug 2026 06:42:30 UTC (36 KB) Full-text links: Access Paper: View a PDF of the paper titled Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints, by N. X. D. Bao and Tan H. 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