Top

Fuzzy Optimization and Decision Making

Published in:

22-04-2015

Relationships between interval-valued vector optimization problems and vector variational inequalities

Authors: Jianke Zhang, Qinghua Zheng, Xiaojue Ma, Lifeng Li

Published in: Fuzzy Optimization and Decision Making | Issue 1/2016

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, we study some relationships between interval-valued vector optimization problems and vector variational inequalities under the assumptions of LU-convex smooth and non-smooth objective functions. We identify the weakly efficient points of the interval-valued vector optimization problems and the solutions of the weak vector variational inequalities under smooth and non-smooth LU-convexity assumptions.

previous article Generalized bipolar product and sum

next article The Karush–Kuhn–Tucker optimality conditions for fuzzy optimization problems

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Ansari, Q. H., & Rezaie, M. (2013). Generalized vector variational-like inequalities and vector optimization in Asplund spaces. Optimization, 62(6), 721–734.CrossRefMathSciNetMATH

Bhurjee, A. K., & Panda, G. (2012). Efficient solution of interval optimization problem. Mathematical Methods of Operations Research, 76, 273–288.CrossRefMathSciNetMATH

Chalco-Cano, Y., Lodwick, W. A., & Rufian-Lizana, A. (2013). Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optimization and Decision Making, 3(12), 305–322.CrossRefMathSciNet

Chen, J. W., Wan, Z., & Chao, Y. J. (2013). Nonsmooth multiobjective optimization problems and weak vector quasi variational inequalities. Computational and Applied Mathematics, 32(2), 291–301.CrossRefMathSciNetMATH

Clarke, F. H. (1983). Optimization and nonsmooth analysis. New York: Wiley.MATH

Giannessi, F. (1980). Theorems of the alternative, quadratic programming and complementarity problems. In R. W. Cottle, F. Giannessi, & J. L. Lions (Eds.), Variational Inequalities and complementarity problems (pp. 151–186). New York: Wiley Press.

Giannessi, F. (2000). Vector variational inequalities and vector equilibria: Mathematical theories. Dordrecht, Holland: Kluwer Academic Publishers.CrossRef

Gupta, A., Mehra, A., & Bhatia, D. (2006). Approximate convexity in vector optimization. Bulletin of the Australian Mathematical Society, 74, 207–218.CrossRefMathSciNetMATH

Jayswal, A., Stancu-Minasian, I., & Ahmad, I. (2011). On sufficiency and duality for a class of interval-valued programming problems. Applied Mathematics and Computation, 218, 4119–4127.CrossRefMathSciNetMATH

Jiang, C., Han, X., & Liu, G. P. (2008). A nonlinear interval number programming method for uncertain optimization problems. European Journal of Operational Research, 188, 1–13.CrossRefMathSciNetMATH

Laha, V., Al-Shamary, B., & Mishra, S. K. (2014). On nonsmooth V-invexity and vector variational- like inequalities in terms of the Michel–Penot subdifferentials. Optimization Letters, 8(5), 1675–1690.CrossRefMathSciNetMATH

Mishra, S. K., Wang, S. Y., & Lai, K. K. (2009). Generalized convexity and vector optimization. Berlin: Springer.

Mishra, S. K., & Laha, V. (2012). On V-r-invexity and vector variational-like inequalities. Filomat, 26(5), 1065–1073.CrossRefMathSciNetMATH

Mishra, S. K., & Laha, V. (2013). A note on the paper on approximately star-shaped functions and approximate vector variational inequalities. Journal of Optimization Theory and Applications, 159, 554–557.CrossRefMathSciNetMATH

Mishra, S. K., & Laha, V. (2013). On approximately star-shaped functions and approximate vector variational inequalities. Journal of Optimization Theory and Applications, 156, 278–293.CrossRefMathSciNetMATH

Mishra, S. K., & Upadhyay, B. B. (2013). Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency. Positivity, 17(4), 1071–1083.CrossRefMathSciNetMATH

Moore, R. E. (1979). Method and applications of interval analysis. Philadelphia: SIAM.CrossRef

Moore, R., & Lodwick, W. (2003). Interval analysis and fuzzy set theory. Fuzzy Sets and Systems, 135(1), 5–9.CrossRefMathSciNetMATH

Ngai, H. V., Luc, D. T., & Thera, M. (2000). Approximate convex functions. Journal of nonlinear and convex analysis, 1, 155–176.MATH

Ruiz-Garzrón, G., Osuna-Grómez, R., & Rufirán-Lizana, A. (2004). Relationships between vector variational-like inequality and optimization problems. European Journal of Operational Research, 157, 113–119.CrossRefMathSciNet

Stefanini, L., & Bede, B. (2009). Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Analysis, 71, 1311–1328.CrossRefMathSciNetMATH

Sun, Y. H., & Wang, L. S. (2013). Optimalty conditions and duality in nondifferentiable interval-valued programming. Journal of Industrial and Managenment Optimation, 9, 131–142.CrossRefMATH

Wu, H.-C. (2007). The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function. European Journal of Operational Research, 176, 46–59.CrossRefMathSciNetMATH

Wu, H.-C. (2009). The Karush–Kuhn–Tucker optimality conditions in multiobjective programming problems with interval-valued objective function. European Journal of Operational Research, 196, 49–60.CrossRefMathSciNetMATH

Yang, X. Q. (1997). Vector variational inequality and vector pseudolinear optimization. Journal of Optimization Theory and Applications, 95, 729–734.CrossRefMathSciNetMATH

Zhang, J. K., Liu, S. Y., Li, L. F., & Feng, Q. X. (2014). The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function. Optimation Letters, 8, 607–631.CrossRefMathSciNetMATH

Title: Relationships between interval-valued vector optimization problems and vector variational inequalities
Authors: Jianke Zhang
Qinghua Zheng
Xiaojue Ma
Lifeng Li
Publication date: 22-04-2015
Publisher: Springer US
Published in: Fuzzy Optimization and Decision Making / Issue 1/2016
Print ISSN: 1568-4539
Electronic ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-015-9212-x

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 1/2016

Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their application

Natural negation of interval-valued t-(co) norms and implications

The Karush–Kuhn–Tucker optimality conditions for fuzzy optimization problems

A unit commitment-based fuzzy bilevel electricity trading model under load uncertainty

Generalized bipolar product and sum

Premium Partner