An inexact scalarization proximal point method for multiobjective quasiconvex minimization

A nonmonotone gradient method for constrained multiobjective optimization problems

“…It is known that the condition {x ∈ C : F(x) F(x k ), ∀ k ∈ N} = / 0 has been frequently used in the convergence analysis of many algorithms for vector optimization, see for example the projected gradient method [9,10,37], steepest descent method [12], proximal point method [14,16,40]. This assumption is related to the completeness of the image of F, namely, all nonincreasing sequences with respect to in the image of F have a lower bound.…”

“…In view of its extensive applications, the research on the numerical algorithms for solving multiobjective optimization problems has received a lot of attention and many iterative methods have been proposed, including projected gradient method [9,10,11], steepest descent method [12,13], proximal point method [14,15,16], conjugate gradient method [17], Newton method [18,19], trust-region method [20,21] and so on.…”