A line search technique for a class of multi-objective optimization problems using subgradient

This paper proposes a line search technique to solve a special class of multi-objective optimization problems in which the objective functions are supposed to be convex but need not be differentiable. This is an iterative process to determine Pareto critical points. A suitable sub-problem is proposed at every iteration of the iterative process to determine the direction vector using the sub-differential of every objective function at that point. The proposed method is verified in numerical examples. This methodology does not bear any burden of selecting suitable parameters like the scalarization methods.