After introducing effective solutions into non-separated multi-objective programming

and by substituting a sufficient large number M

i

for f

i

(x) which can not be found in the multi-object function

the authors have translated non-separated multi-objective programming into general multi-objective programming problem

and have established some criteria for identifying the effective solutions to non-separated multi-objective programming problem.The research has promoted the conditions proposed by Fritz-John and Kuhn-Tucker.