The cosine measure of a set of vectors in \(\mathbb{R}^n\) measures how well the set covers all directions in \(\mathbb{R}^n\). It identifies the direction furthest, in angle, from the set. It is used in the convergence theory of various optimization algorithms, but also highlights interesting geometric properties of sets. For example, the cosine measure of … Read more
We propose in this paper a Polak-Ribière-Polyak conjugate gradient type method for solving bicriteria optimization problems by avoiding scalarization techniques. Two particular advantages in this contribution are to be noted. First, the suggested descent direction common to both criteria may be directly computed by a given formula without solving any intermediate subproblem. Second, the descent … Read more
In this paper we propose a spectral Fletcher-Reeves conjugate gradient-like method (SFRCG) for solving unconstrained bi-criteria minimisation problems without using any technique of scalarization. We suggest an explicit formulae for computing a descent direction common to both criteria. This latter verifies furthermore a sufficient descent property which does not depend on the line search nor … Read more