where An is the n-fold product of the σ-algebra A of subsets of a given set X , Fi, Gi, i∈ p ≡ {1,2, . . . , p}, and Hj , j ∈ q, are real-valued functions defined on An, and for each i∈ p, Gi(S) > 0 for all S∈An such that Hj(S) ≤ 0, j ∈ q. Optimization problems of this type in which the functions Fi, Gi, i∈ p, and Hj , j ∈ q, are defined on a subset of Rn (n-dimensional Euclidean space) are cal...

multi objective quadratic fractional programming (moqfp) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the object...

a procedure is presented that synthesizes fractional crystallization separation processes to obtain pure solids from multi-component solutions. the method includes a procedure to generate a network flow model to identify alternative process designs for fractional crystallization. the main advantage of this systematic procedure with respect to other reported procedures is using non-equilibrium s...

In this paper a new concept of duality is given for the linear fractional programming (LFP) problem in which the objective function is a linear fractional function and where the constraint functions are in the form of linear inequalities. Our result is based on transforming the linear fractional programming problem to an equivalent linear programming with the same dimension. A simple example is...

Multi objective quadratic fractional programming (MOQFP) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the objecti...