Autori
Recchioni, Maria CristinaMiglierina, EnricoMolho, ElenaTitolo
Box-constrained vector optimization: a steepest descent method without "apriori" scalarizationPeriodico
Università degli Studi dell'Insubria. Dipartimento di Economia. Quaderni di ricercaAnno:
2006 - Fascicolo:
3 - Pagina iniziale:
1 - Pagina finale:
20In this paper a notion of descent direction for a vector function defined
on a box is introduced. This concept is based on an appropriate convex combination
of the “projected” gradients of the components of the objective functions. The
proposed approach does not involve an “apriori” scalarization since the coefficients
of the convex combination of the projected gradients are the solutions of a suitable
minimization problem depending on the feasible point considered. Subsequently, the
descent directions are considered in the formulation of a first order optimality condition
for Pareto optimality in a box-constrained multiobjective optimization problem.
Moreover, a computational method is proposed to solve box-constrained multiobjective
optimization problems. This method determines the critical points of the box
constrained multiobjective optimization problem following the trajectories defined
through the descent directions mentioned above. The convergence of the method to
the critical points is proved. The numerical experience shows that the computational
method efficiently determines the whole local Pareto front.
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