Continuous OptimizationNonmonotone gradient methods for vector optimization with a portfolio optimization application

•Vector optimization is studied.•Two nonmonotone gradient algorithms are proposed for vector optimization.•The global and local convergence results for the new algorithms are presented.•The efficiency of the new algorithm is shown by an application to a portfolio optimization problem.

This paper proposes two nonmonotone gradient algorithms for a class of vector optimization problems with a C−convex objective function. We establish both the global and local convergence results for the new algorithms. We then apply the new algorithms to a portfolio optimization problem under multi-criteria considerations.