Solution analysis of multi-objective programming problem

Weighted ideal point method converts a multi-objective programming problem into a single objective programming problem. Solving corresponding single objective programming problem, some Pareto optimal solutions of the original multi-objective programming problem can be found. Specially, for convex multi-objective programming problems, we prove that there exist weights such that Pareto optimal solution is the optimal solution of the corresponding single objective programming problem. This means that all Pareto optimal solutions can be found. At last, an example is given to illustrate that all Pareto optimal solutions of convex multi-objective programming problems can be found by the weighted ideal point method.