A barrier-type method for multiobjective optimization

Abstract

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 analyse its convergence to Pareto or weak Pareto solutions.

Keywords:

• Barrier methods
• multiobjective optimization
• Pareto optimality

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Kyoto University Foundation, a Grant-in-Aid for Young Scientists (B) (26730012) from National Council for Scientific and Technological Development (CNPq).