A barrier-type method for multiobjective optimization

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 … Read more

Cutting Box Strategy: an algorithmic framework for improving metaheuristics for continuous global optimization

In this work, we present a new framework to increase effectiveness of metaheuristics in seeking good solutions for the general nonlinear optimization problem, called Cutting Box Strategy (CBS). CBS is based on progressive reduction of the search space through the use of intelligent multi-starts, where solutions already obtained cannot be revisited by the adopted metaheuristic. … Read more

An external penalty-type method for multicriteria

We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued … Read more

A quadratically convergent Newton method for vector optimization

We propose a Newton method for solving smooth unconstrained vector optimization problems under partial orders induced by general closed convex pointed cones. The method extends the one proposed by Fliege, Grana Drummond and Svaiter for multicriteria, which in turn is an extension of the classical Newton method for scalar optimization. The steplength is chosen by … Read more