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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.
📌 3 Key Takeaways
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Objective & Hypothesis:Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem.
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Key Findings & Data:In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation.
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Conclusion & Impact:Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Set-valued optimization · nonconvex optimization · vectorization
Abstract
Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.
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Cite This Article
KARAMAN, E., GÜVENÇ, İ. A., SOYERTEM, M., TOZKAN, D., KÜÇÜK, M., KÜÇÜK, Y. (2022). A vectorization for nonconvex set-valued optimization. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 4, 1815–1832. https://ajindex.com/articles/604635