A conjugate directions-type procedure for quadratic multiobjective optimization

We propose an extension of the real-valued conjugate directions method for unconstrained quadratic multiobjective problems. As in the single-valued counterpart, the procedure requires a set of directions that are simultaneously conjugate with respect to the positive definite matrices of all quadratic objective components. Likewise, the multicriteria version computes the steplength by means of the unconstrained minimization of a single-variable strongly convex function at each iteration. When it is implemented with a weakly-increasing (strongly-increasing) auxiliary function, the scheme produces weak Pareto (Pareto) optima in finitely many iterations.

Automated summary

The proposed extension of the real-valued conjugate directions method is used for unconstrained quadratic multiobjective problems, aiming to find weak Pareto and Pareto optima through specific steps and calculations in each iteration.