FUZZY LINEAR PROGRAMMING PROBLEM USING POLYNOMIAL  PENALTY METHOD

A Nagoor  Gani; R Yogarani

doi:10.48165/

Authors

A Nagoor Gani P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu 620020, India.
R Yogarani Department of Mathematics, Arul Anandar College, Madurai, Tamil Nadu 625514, India.

DOI:

https://doi.org/10.48165/

Keywords:

Fuzzy Linear Programming, triangular fuzzy number, polynomial penalty method, polynomial order even

Abstract

In this paper we focus on a polynomial order even penalty function for solving a fuzzy linear programming problem and develop an algorithm which gives a better rate of convergence to achieve the optimal solution to the problem in hand. Some numerical examples are included to exhibit the efficiency of the new algorithmic procedure developed by us.

References

. Betts, J.T. (1975). An improved penalty function method for solving constrained parameter optimization problems, Journal of Optimization Theory and Applications, 16 (1-2), 1-24.

. Bertsekas, Dimitri P. (1973). Convergence rate of penalty and multiplier methods, Decision and Control including the 12th Symposium on Adaptive Processes, 1973 IEEE Conference, Vol. 12. IEEE, 1973, 260-264.

. Bertsekas, Dimitri P. (1975). Combined primal-dual and penalty methods for constrained minimization, SIAM Journal on Control, 13(3), 521-544.

. Buckley, J.J. (1988). Possibilistic linear programming with triangular fuzzy numbers, Fuzzy Sets and Systems, 26 (1), 135-138.

. Douglas, Jim, and Dupont, Todd (1976). Interior penalty procedures for elliptic and parabolic Galerkin methods, Computing Methods in Applied Sciences, Springer, Berlin, Heidelberg, 207-216. [6]. Durazzi, C. (2000). On the Newton interior-point method for nonlinear programming problems, Journal of Optimization Theory and Applications, 104 (1), 73-90.

. El-Bakry, A. S., Tapia, Richard A., Tsuchiya, T. and Zhang, Yin (1996). On the formulation and theory of the Newton interior-point method for nonlinear programming, Journal of Optimization Theory and Applications, 89(3), 507-541.

. Fiacco, Anthony V. (1976). Sensitivity analysis for nonlinear programming using penalty methods, Mathematical Programming, 10(1), 287-311.

. Nagoor Gani, A. and Assarudeen, S.N. Mohamed (2012). A new operation on triangular fuzzy number for solving fuzzy linear programming problem, Applied Mathematical Sciences, 6(11), 525-532.

. Hsieh, Chih Hsun and Shan-Huo Chen (1999). Similarity of generalized fuzzy numbers with graded mean integration representation, Proc. 8th Int. Fuzzy Systems Association World Congr., Vol. 2, 551- 555.

. Inuiguchi, Masahiro, and Tanino, Tetsuzo (2004). Fuzzy linear programming with interactive uncertain parameters, Reliable Computing, 10(5), 357-367.

. Kas, Péter, Klafszky, Emil and Mályusz, Levente (1999). Convex program based on the Young inequality and its relation to linear programming, Central European Journal for Operations Research, 7(3) , 291-304.

. Parwadi, M., Mohd., I.B. and Ibrahim, N.A. (2002). Solving Bounded LP Problems using Modified Logarithmic-exponential Functions, Proceedings of the National Conference on Mathematics and Its Applications in UM Malang. 2002, 135-141.

. Ramík, Jaroslav (1985). Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets and Systems, 16(2), 123-138.

. Tanaka, H. and Asai, K. (1984). Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems, 13(1), 1-10.

. Vanderbei, Robert J., and Shanno, David F. (1999). An interior-point algorithm for nonconvex nonlinear programming, Computational Optimization and Applications, 13(1-3), 231-252. [17]. Wright, Stephen J. (2001). On the convergence of the Newton/log-barrier method, Mathematical Programming, 90(1), 71-100.

. Yeniay, Özgür (2005). Penalty function methods for constrained optimization with genetic algorithms, Mathematical and Computational Applications, 10(1), 45-56.

. Zboon, Radhi A., Yadav, Shiv Prasad and Mohan, C. (1999). Penalty method for an optimal control problem with equality and inequality constraints, Indian Journal of Pure and Applied Mathematics, 30, 1-14.

. Zimmermann, H.J. (1978). Fuzzy programming and linear programming with several objective Functions, Fuzzy Sets and Systems, 1(1), 45-55.

. Dubois, Didier, and Prade, Henri (1987). The mean value of a fuzzy number, Fuzzy Sets and Systems, 24(3), 279-300.

. Nezam, Mahdavi-Amiri, Nasseri, Seyed Hadi and Yazdani, Alahbakhsh(2009). Fuzzy primal simplex algorithms for solving fuzzy linear programming problems, Iranian Journal of Operations Research, 1(2), 68-84.