An incremental descent method for multi-objective optimization. (4th March 2023) - Oliveira, Ivo F. D.; Takahashi, Ricardo H. C.
ABSTRACT: Multi-objective steepest descent, under the assumption of lower-bounded objective functions with L -Lipschitz continuous gradients, requires O ( m / ϵ 2 ) gradient and function computations to produce a measure of proximity to critical conditions akin to | | ∇ f ( x ) | | ≤ ϵ in the single-objective setting, where m is the number of objectives considered. We reduce this to O ( 1 / ϵ 2 ) with a multi-objective incremental approach that has a computational cost that does not grow with the number of objective functions m .