finding properly efficient solutions of nonconvex multiobjective optimization problems with a minimum bound for trade-offs

In the presented paper, we investigate efficient solutions to optimization problems with multiple criteria and bounded trade-offs. a nonlinear optimization problem to find the relationships between the upper bound for trade-offs and objective functions is presented. due to this problem, we determine some properly efficient points that are closer to the ideal point. to this end,  we apply the extended form of the generalized tchebycheff norm. note that all the presented results work for general problems and no convexity assumption is needed.