Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds

Details Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds

2010-10-29

arxiv.org/abs/1011.0010v1

Mathematics

Numerical Analysis

20 pages; paper submitted to Proceedings of the London Mathematical Society on march 01, 2010

Scientific paper

In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by the method is guaranteed. Under mild assumptions on the multicriteria function, we prove that each accumulation point (if they exist) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming quasi-convexity of the multicriteria function and non-negative curvature of the Riemannian manifold, we prove full convergence of the sequence to a Pareto critical.

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