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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2014 / Cilt: 4 - Sayı: 1

Vector variational inequalities and their relations with vector optimization

Surjeet Kaur SUNEJAA
Bhawna KOHLİ
Pages
35–44
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In the end we study the interrelations between these with the help of strict K -naturally quasimonotonicity of Clarke subdifferential map.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, K - c quasiconvex, K - c pseudoconvex and other related functions have been introduced in terms of their Clarke subdifferentials, where K is an arbitrary closed convex, pointed cone with nonempty interior.
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Key Findings & Data:The (strict, weakly) K -pseudomonotonicity, (strict) K -naturally quasimonotonicity and K -quasimonotonicity of Clarke subdifferential maps have also been defined.
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Conclusion & Impact:In the end we study the interrelations between these with the help of strict K -naturally quasimonotonicity of Clarke subdifferential map.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, K - c quasiconvex, K - c pseudoconvex and other related functions have been introduced in terms of their Clarke subdifferentials, where K is an arbitrary closed convex, pointed cone with nonempty interior. The (strict, weakly) K -pseudomonotonicity, (strict) K -naturally quasimonotonicity and K -quasimonotonicity of Clarke subdifferential maps have also been defined. Further, we introduce Minty weak (MVVIP) and Stampacchia weak (SVVIP) vector variational inequalities over arbitrary cones. Under regularity assumption, we have proved that a weak minimum solution of vector optimization problem (VOP) is a solution of (SVVIP) and under the condition of K - c pseudoconvexity we have obtained the converse for MVVIP (SVVIP). In the end we study the interrelations between these with the help of strict K -naturally quasimonotonicity of Clarke subdifferential map.

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Cite This Article

SUNEJAA, S. K., KOHLİ, B. (2022). Vector variational inequalities and their relations with vector optimization. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 4 - Sayı: 1, 35–44. https://ajindex.com/articles/440718

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