  For solving constrained multicriteria problems, we introduce the
multiobjective barrier method (MBM), which extends the scalar-valued internal
penalty method. This multiobjective version of the classical method also
requires a penalty barrier for the feasible set and a sequence of nonnegative
penalty parameters. Differently from the single-valued procedure, MBM is
implemented by means of an auxiliary "monotonic" real-valued mapping, which may
be chosen in a quite large set of functions. Here, we consider problems with
continuous objective functions, where the feasible sets are defined by finitely
many continuous inequalities. Under mild assumptions, and depending on the
monotonicity type of the auxiliary function, we establish convergence to Pareto
or weak Pareto optima. Finally, we also propose an implementable version of MBM
for seeking local optima and analyze its convergence to Pareto or weak Pareto
solutions.
