Aplikasi metoda subgradient untuk menyelesaikan program linear fuzzy=Applied subgradient methods for solving fuzzy linear programming

• Main Author: Perpustakaan UGM, i-lib
• Format: Article NonPeerReviewed
• Published: [Yogyakarta] : Universitas Gadjah Mada 2005
• Subjects: Jurnal i-lib UGM
• Online Access: https://repository.ugm.ac.id/17810/; http://i-lib.ugm.ac.id/jurnal/download.php?dataId=578
• Institution: Universitas Gadjah Mada

In this paper we shall present subgradient method for solving two kinds of fuzzy linear programming problems with linear membership functions, i.e., linear programming with constraint coefficients and linear programming with resources and constraint coefficients are fuzzy numbers. Subgradient method is based on the construction of dual problems by using Augmented Lagrangian functions which can be applied for solving a large class of non-convex and non-smooth constrained optimization problems. In this method we do not use any convexity and differentiability conditions. The value of the dual function strongly increase at each iteration and the Convergence Theorem for the method is also presented. On the other hand, the crisp problems obtained after the deffuzification are nonlinear and even nonconvex in general such that subgradient method is used to solve these problems. Key words : Subgradient methods, Lagrangian duality, Non-convex nonlinear programming, Fuzzy linear programming.