  We study a general scalarization approach via utility functions in
multi-objective optimization. It consists of maximizing utility which is
obtained from the objectives' bargaining with regard to a disagreement
reference point. The theoretical framework for a broad class of utility
functions from microeconomics is developed. For that, we associate a
utility-dependent single-objective optimization problem with the given
multi-objective optimization problem. We show that Pareto optimal points of the
latter can be recovered by solving the former. In particular, Cobb-Douglas,
Leontief, and CES utility functions are considered. We prove that any Pareto
optimal point can be obtained as a solution of scalarization via one of the
mentioned utility functions. Further, we propose a numerical scheme to solve
utility-dependent single-objective optimization problems. Here, the main
difficulty comes from the necessity to address constraints which are associated
with a disagreement reference point. Our crucial observation is that the
explicit treatment of these additional constraints may be avoided. This is the
case if the Slater condition is satisfied and the utility function under
consideration has the so-called barrier property. Under these assumptions, we
prove the convergence of our scheme to Pareto optimal points. Numerical
experiments on real-world financial datasets in a portfolio selection context
confirm the efficiency of our scalarization approach via utility functions.
