A SUBGRADIENT METHOD FOR VECTOR OPTIMIZATION PROBLEMS

Vector optimization problems are a significant extension of scalar optimization and have many real life applications. We consider an extension of the projected subgradient method to convex vector optimization, which works directly with vector-valued functions, without using scalar-valued objectives. We eliminate the scalarization approach, a popular strategy for solving vector optimization problems, exploring strongly the structure of these kinds of problems. Under suitable assumptions, we show that the sequence generated by the algorithm converges to a weakly efficient optimum point.