Global solutions to fractional programming problem with ratio of nonconvex functions

Global solutions to fractional programming problem with ratio of nonconvex functions

This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in R. By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R that exhibits no duality gap....

FGP approach to multi objective quadratic fractional programming problem

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...

Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach

In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision ...

Global optimization of fractional posynomial geometric programming problems under fuzziness

In this paper we consider a global optimization approach for solving fuzzy fractional posynomial geometric programming problems. The problem of concern involves positive trapezoidal fuzzy numbers in the objective function. For obtaining an optimal solution, Dinkelbach’s algorithm which achieves the optimal solution of the optimization problem by means of solving a sequence of subproblems ...

To “ Global Solutions to Folded Concave Penalized Nonconvex Learning ”