An Inexact Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds
In this paper, we present an inexact version of the steepest descent method with Armijos rule for multicriteria optimization in the Riemannian context given in Bento etal. (J.Optim. Theory Appl., 154: 88107, 2012). Under mild assumptions on the multicriteria function, we prove that each accumulation point (if any) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming that the multicriteria function is quasi-convex and the Riemannian manifold has nonnegative curvature, we show full convergence of any sequence generated by the method to aPareto critical point.
steepest descent multicriteria optimization riemannian manifolds pareto optimality quasi-convexity quasi-fejr convergence