具有椭球不确定性集的不确定lcp间隙函数公式$$\Gamma $$ -鲁棒对应物解的存在性

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Lulin Tan, Wei Hong Yang, Jinbiao Pan
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引用次数: 0

摘要

本文给出了不确定线性互补问题间隙函数公式\(\Gamma \) -鲁棒对应物解的存在性定理,其中\(\Gamma \)根据解的保守性水平调节模型的鲁棒性。如果\(\Gamma \) -鲁棒不确定性集是非凸的,则很难证明对应鲁棒不确定性集解的存在性。利用渐近函数技术,建立了相应鲁棒对应物解的存在性定理。对于非凸\(\Gamma \) -鲁棒椭球不确定性集,本文[Krebs et al., Int.]没有证明这些存在性结果。译:哦。Res. 29(2022),第417-441页];对于凸\(\Gamma \) -鲁棒椭球不确定性集,在较Krebs论文弱得多的条件下得到了存在性定理。最后,以不确定交通均衡问题为例,说明了非凸不确定性集对鲁棒解保守性水平的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Existence of solutions to $$\Gamma $$ -robust counterparts of gap function formulations of uncertain LCPs with ellipsoidal uncertainty sets

Existence of solutions to $$\Gamma $$ -robust counterparts of gap function formulations of uncertain LCPs with ellipsoidal uncertainty sets

In this paper, we give some existence theorems of solutions to \(\Gamma \)-robust counterparts of gap function formulations of uncertain linear complementarity problems, in which \(\Gamma \) plays a role in adjusting the robustness of the model against the level of conservatism of solutions. If the \(\Gamma \)-robust uncertainty set is nonconvex, it is hard to prove the existence of solutions to the corresponding robust counterpart. Using techniques of asymptotic functions, we establish existence theorems of solutions to the corresponding robust counterpart. For the case of nonconvex \(\Gamma \)-robust ellipsoidal uncertainty sets, these existence results are not proved in the paper [Krebs et al., Int. Trans. Oper. Res. 29 (2022), pp. 417–441]; for the case of convex \(\Gamma \)-robust ellipsoidal uncertainty sets, our existence theorems are obtained under the conditions which are much weaker than those in Krebs’ paper. Finally, a case study for the uncertain traffic equilibrium problem is considered to illustrate the effects of nonconvex uncertainty sets on the level of conservatism of robust solutions.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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