La programación lineal sobre subconjuntos difusos, definida por Zimmermann, se desarrolla en estrecha relación con la definición de las funciones pertinentes funciones de pertenencia. Se estudia la dualidad difusa, ligada a la dualidad en los problemas de programación lineal con multicriterios.
The present article explores the way -approximated method is applied to substantiate duality results for the fractional variational problems under invexity. -approximated dual pair is engineered and a careful study of the original dual pair has been done to establish the duality results for original problems. Moreover, an appropriate example is constructed based on which we can validate the established dual statements. The paper includes several recent results as special cases.
2000 Mathematics Subject Classification: 90C48, 49N15, 90C25In this paper we reconsider a nonconvex duality theory established by B. Lemaire and M. Volle (see [4]), related to a primal problem of minimizing the difference of two convex functions subject to a DC-constraint. The purpose of this note is to present a new method based on Toland-Singer duality principle. Applications to the case when the constraints are vector-valued are provided.
Duality of linear programming is used to establish an important duality theorem for a class of non-linear programming problems. Primal problem has quasimonotonic objective function and a convex polyhedron as its constraint set.