The Regularized Newton Method for Multiobjective Optimization

In this paper, we introduce the regularized Newton method for multiobjective optimization. The method does not scalarize the original multiobjective optimization problem. For any vector convex function, with a compact level set, the regularized Newton method generates a sequence that converges to the optimal points from any starting point. Moreover the regularized Newton method does not require strong convexity property in the entire space.