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On second-order Karush--Kuhn--Tucker optimality conditions for $C^{1,1}$ vector optimization problems

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Nguyen Van Tuyen

Optimization and Control · Submitted 2 Mar 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The obtained results improve existing ones in the literature.

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arXiv ID2503.00927 (version 1)
Pith IDFBDBCA5U, Pith's permanent record of this paper and its review
CitationNguyen Van Tuyen. "On second-order Karush--Kuhn--Tucker optimality conditions for $C^{1,1}$ vector optimization problems." arXiv:2503.00927 (2025). https://pith.science/paper/FBDBCA5U
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,176 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.69 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

This paper focuses on optimality conditions for $C^{1,1}$ vector optimization problems with inequality constraints. By employing the limiting second-order subdifferential and the second-order tangent set, we introduce a new type of second-order constraint qualification in the sense of Abadie. Then we establish some second-order necessary optimality conditions of Karush--Kuhn--Tucker-type for local (weak) efficient solutions of the considered problem. In addition, we provide some sufficient conditions for a local efficient solution of the such problem. The obtained results improve existing ones in the literature.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper focuses on optimality conditions for $C^{1,1}$ vector optimization problems with inequality constraints. background 0.86 0.50 0.05 asserted 0.96
s1 By employing the limiting second-order subdifferential and the second-order tangent set, we introduce a new type of second-order constraint qualification in the sense of Abadie. contribution 0.65 0.94 0.08 asserted 1.00
s2 Then we establish some second-order necessary optimality conditions of Karush--Kuhn--Tucker-type for local (weak) efficient solutions of the considered problem. result 0.84 0.96 0.40 asserted 1.00
s3 In addition, we provide some sufficient conditions for a local efficient solution of the such problem. result 0.57 0.96 0.14 asserted 1.00
s4 The obtained results improve existing ones in the literature. interpretation 0.81 0.66 0.31 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper focuses on optimality conditions for $C^{1,1}$ vector optimization problems with inequality constraints. By employing the limiting second-order subdifferential and the second-order tangent set, we introduce a new type of second-order constraint qualification in the sense of Abadie. Then we establish some second-order necessary optimality conditions of Karush--Kuhn--Tucker-type for local (weak) efficient solutions of the considered problem. In addition, we provide some sufficient conditions for a local efficient solution of the such problem. The obtained results improve existing ones in the literature.

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