Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity
Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity
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DOI：
10.1016/j.chaos.2023.113834
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发表时间：
2023-09
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影响因子：
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通讯作者：
Yating Guo;G. Ye;Wei Liu;Dafang Zhao;S. Treanțǎ
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文献类型：
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作者：
Yating Guo;G. Ye;Wei Liu;Dafang Zhao;S. Treanțǎ
本文重点研究非光滑非凸区间值优化问题。为此，我们根据对称 gH 可微区间值函数提出区间值对称无凸性、区间值对称伪无凸性和区间值对称拟无凸性。还讨论了这些广义凸性的一些重要性质。通过利用这些新概念，我们为所考虑的问题建立了足够的卡鲁什-库恩-塔克条件。此外，将Wolfe和Mond-Weir型对偶问题关联起来，并导出了弱、强和严格逆对偶结果。最后，我们将所发展的理论应用到支持向量机的区间数据二元分类问题。
This paper focuses on a nonsmooth nonconvex interval-valued optimization problem. For this, we propose interval-valued symmetric invexity, interval-valued symmetric pseudo-invexity and interval-valued symmetric quasi-invexity in terms of the symmetric gH-differentiable interval-valued functions. Some important properties of these generalized convexities are also discussed. By utilizing these new concepts, we establish sufficient Karush–Kuhn–Tucker conditions for the considered problem. Further, the Wolfe and Mond–Weir type dual problems are associated and weak, strong and strict converse duality results have been derived. Finally, we apply the developed theory to a binary classification problem of interval data by support vector machine.