A fuzzy linear basis algorithm for nonlinear separable programming problems

In the paper we develop a theory of fuzzy linear bases. The theory is usefu l for transforming nonlinear separable programming problems (NLSP) into a f inite sequence of fuzzy linear programming relaxations at a given level of accuracy epsilon. The key concepts of the theory are fuzzy linear interpola tion and the maximal profile of the polyhedron generated from a set of brea k points for each variable dimension. The maximal profile is divided into a djacent convex sub-intervals, in which the nonlinear problem is transformed into a sequence of fuzzy linear sub-problems. All discontinuities are equi pped with a break point, whereby the Fuzzy Linear Basis (FLB) Algorithm is applicable to separable NLPs with a finite number of discontinuities. We pr ove that the solution to the original nonlinear problem is included in the sequence of fuzzy linear subproblems at the prespecified accuracy epsilon. The principles of the Fuzzy Linear Basis Algorithm are illustrated in an ex ample. (C) 2001 Elsevier Science B.V. All rights reserved.