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Journal of Applied Mathematics and Computing

Erschienen in:

02.11.2017 | Original Research

A saddle point characterization of efficient solutions for interval optimization problems

verfasst von: Debdulal Ghosh, Debdas Ghosh, Sushil Kumar Bhuiya, Lakshmi Kanta Patra

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2018

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Abstract

In this article, we attempt to characterize efficient solutions of constrained interval optimization problems. Towards this aim, at first, we study a scalarization characterization to capture efficient solutions. Then, with the help of saddle point of a newly introduced Lagrangian function, we investigate efficient solutions of an interval optimization problem. Several parts of the results are supported with numerical and pictorial illustration.

Vorheriger Artikel On the least distance eigenvalues of the second power of a graph

Nächster Artikel A new family of conjugate gradient methods for unconstrained optimization

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Bhurjee, A.K., Panda, G.: Efficient solution of interval optimization problems. Math. Methods Oper. Res. 76(3), 273–288 (2012)MathSciNetCrossRefMATH

Chakraborty, D., Ghosh, D.: Analytical fuzzy plane geometry II. Fuzzy Sets Syst. 243, 84–10 (2014)MathSciNetCrossRefMATH

Chalco-Cano, Y., Lodwick, W.A., Rufian-Lizana, A.: Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optim. Decis. Mak. 12(3), 305–322 (2013)MathSciNetCrossRef

Chen, S.H., Wu, J., Chen, Y.D.: Interval optimization for uncertain structures. Finite Elem. Anal. Des. 40, 1379–1398 (2004)CrossRef

Cheng, J., Liu, Z., Wu, Z., Tang, M., Tan, J.: Direct optimization of uncertain structures based on degree of interval constraint violation. Comput. Struct. 164, 83–94 (2016)CrossRef

Chalco-Cano, Y., Rufian-Lizana, A., Roman-Flores, H., Jimenez-Gamero, M.D.: Calculus for interval-valued functions using generalized Hukuhara derivative and applications. Fuzzy Sets Syst. 219, 49–67 (2013)MathSciNetCrossRefMATH

Frits, E.R., Rev, E., Lelkes, Z., Markot, M., Csendes, T.: Application of an interval optimization method for studying feasibility of batch extractive distillation. In: Proceedings of the International Workshop on Global Optimization, Almeria, pp. 103–108 (2005)

Ghosh, D.: Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions. J. Appl. Math. Comput. 53, 709–731 (2016)MathSciNetCrossRefMATH

Ghosh, D.: A Newton method for capturing efficient solutions of interval optimization problems. Opesearch 53, 648–665 (2017)MathSciNetCrossRefMATH

10.

Ghosh, D., Chakraborty, D.: Analytical fuzzy plane geometry I. Fuzzy Sets Syst. 209, 66–83 (2012)MathSciNetCrossRefMATH

11.

Ghosh, D., Chakraborty, D.: Analytical fuzzy plane geometry III. Fuzzy Sets Syst. 283, 83–107 (2016)MathSciNetCrossRefMATH

12.

Ghosh, D., Chakraborty, D.: A method for capturing the entire fuzzy non-dominated set of a fuzzy multi-criteria optimization problem. J. Intell. Fuzzy Syst. 26, 1223–1234 (2014)MATH

13.

Ghosh, D., Chakraborty, D.: A new Pareto set generating method for multi-criteria optimization problems. Oper. Res. Lett. 42, 514–521 (2014)MathSciNetCrossRef

14.

Ghosh, D., Chakraborty, D.: A method for capturing the entire fuzzy non-dominated set of a fuzzy multi-criteria optimization problem. Fuzzy Sets Syst. 272, 1–29 (2015)MathSciNetCrossRefMATH

15.

Ghosh, D., Chakraborty, D.: Quadratic interpolation technique to minimize univariable fuzzy functions. Int. J. Appl. Comput. Math. 3(2), 527–547 (2017)MathSciNetCrossRef

16.

Hong, F.-X., Li, D.-F.: Nonlinear programming method for interval-valued \(n\)-person cooperative games. Oper. Res. Int. J. 17(2), 479–497 (2017)MathSciNetCrossRef

17.

Kumar, P.: Inventory model with price-dependent demand rate and no shortages: an interval-valued linear fractional programming approach. Oper. Res. Appl. Int. J. 2(4), 1–14 (2015)

18.

Oliveria, C., Antunes, C.H.: Multiple objective linear programming models with interval coefficients-an illustrated review. Eur. J. Oper. Res. 181, 1434–1463 (2007)CrossRefMATH

19.

Singh, D., Dar, B.A., Goyal, A.: KKT optimality conditions for interval-valued optimization problems. J. Nonlinear Anal. Optim. 5(2), 91–103 (2014)MathSciNet

20.

Wang, H., Zhang, R.: Optimality conditions and duality for arcwise connected interval optimization problems. Opsearch 52(4), 870–883 (2015)MathSciNetCrossRefMATH

21.

Wu, H.C.: The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function. Eur. J. Oper. Res. 176(1), 46–59 (2007)MathSciNetCrossRefMATH

22.

Wu, H.C.: Dulity theory for optimization problems with interval-valued objective fuction. J. Optim. Theory Appl. 144(3), 615–628 (2010)MathSciNetCrossRef

23.

Wu, H.C.: Duality theory in interval-valued linear programming problems. J. Optim. Theory Appl. 150, 298–316 (2011)MathSciNetCrossRefMATH

24.

Ying, Z.-Y., Xi, Y.-G., Zhang, Z.-J.: Test on reachability of a Robot to an object. In: The Proceedings of IEEE International Conference on Robotics and Automation, IEEE Xplore (2002)

25.

Zhang, J., Liu, S., Li, L., Feng, Q.: The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function. Optim. Lett. 8(2), 607–631 (2012)MathSciNetCrossRefMATH

Titel: A saddle point characterization of efficient solutions for interval optimization problems
verfasst von: Debdulal Ghosh
Debdas Ghosh
Sushil Kumar Bhuiya
Lakshmi Kanta Patra
Publikationsdatum: 02.11.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2018
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-017-1140-1

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