On ε-optimality conditions for multiobjective fractional optimization problems
Moon Hee Kim, Gwi Soo Kim, Gue Myung Lee · Fixed Point Theory and Applications · 2011
Abstract A multiobjective fractional optimization problem (MFP), which consists of more than two fractional objective functions with convex numerator functions and convex denominator functions, finitely many convex constraint functions, and a geometric constraint set, is considered. Using parametric approach, we transform the problem (MFP) into the non-fractional multiobjective convex optimization problem (NMCP) v with parametric v ∈ ℝ p , and then give the equivalent relation between (weakly) ε-efficient solution of (MFP) and (weakly) "Equation missing"-efficient solution of "Equation missing". Using the equivalent relations, we obtain ε- optimality conditions for (weakly) ε- efficient solution for (MFP). Furthermore, we present examples illustrating the main results of this study. 2000 Mathematics Subject Classification: 90C30, 90C46.