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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2016 / Cilt: 6 - Sayı: 1

Generalized (?,?)-convexity in nonsmooth vector optimization over cones

Sunila SHARMA
Malti KAPOOR
S. K. SUNEJA
Pages
1–8
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

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

Further, we prove duality results for both Wolfe and Mond-Weir type duals under various types of cone-generalized (?,?)-convexity assumptions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, new classes of cone-generalized (?,?)-convex functions are introduced for a nonsmooth vector optimization problem over cones, which subsume several known studied classes.
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Key Findings & Data:Using these generalized functions, various sufficient Karush-Kuhn-Tucker (KKT) type nonsmooth optimality conditions are established wherein Clarke's generalized gradient is used.
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Conclusion & Impact:Further, we prove duality results for both Wolfe and Mond-Weir type duals under various types of cone-generalized (?,?)-convexity assumptions.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, new classes of cone-generalized (?,?)-convex functions are introduced for a nonsmooth vector optimization problem over cones, which subsume several known studied classes. Using these generalized functions, various sufficient Karush-Kuhn-Tucker (KKT) type nonsmooth optimality conditions are established wherein Clarke's generalized gradient is used. Further, we prove duality results for both Wolfe and Mond-Weir type duals under various types of cone-generalized (?,?)-convexity assumptions.

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Cite This Article

SHARMA, S., KAPOOR, M., SUNEJA, S. K. (2022). Generalized (?,?)-convexity in nonsmooth vector optimization over cones. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 6 - Sayı: 1, 1–8. https://ajindex.com/articles/440696

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References (10)

  1. Antczak, T., On nonsmooth (?,?)- invexmultiobjective programming in finitedimensional Euclidean spaces, Journal of Advanced Mathematical Studies, 7, 127-145 (2014)
  2. Antczak, T., Stasiak, A., (?,?)-invexity in nonsmooth optimization, Numerical Functional Analysis and Optimization, 32(1), 1-25 (2010)
  3. Caristi, G., Ferrara, M., Stefanescu, A., Mathematical programming with (?,?)- invexity. In: Konnov, I.V., Luc, D.T., Rubinov, A.M. (eds.) Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, 583, 167-176. Springer, Berlin-Heidelberg-New York (2006)
  4. Clarke, F. H., Optimization and Nonsmooth Analysis, Wiley, New York (1983)
  5. Craven, B. D., Nonsmooth multiobjective programming, Numerical Functional Analysis and Optimization, 10(1-2), 49-64 (1989)
  6. Ferrara, M., Stefanescu, M.V., Optimality conditions and duality in multiobjective programming with (?,?)-invexity. Yugoslav Journal of Operations Research, 18, 153-165 (2008
  7. Hanson, M.A., On sufficiency of the KuhnTucker conditions, Journal of Mathematical Analysis and Applications, 80, 545-550 (1981)
  8. Hanson, M.A., Mond, B., Further generalization of convexity in mathematical programming. Journal of Information and Optimization Sciences, 3, 25-32 (1982)
  9. Preda, V., On efficiency and duality for multiobjective programs, Journal of Mathematical Analysis and Applications, 166, 365-377 (1992)
  10. Vial, J.P., Strong and weak convexity of sets and functions, Mathematics of Operations Research, 8, 231-259 (1983).