Adaptive Cubic Regularization Methods for Solving Non-convex Multi-objective Optimization Problem 

Huanhuan Yang

College of Mathematics and Information Science, Hebei University, Baoding, 071002, China 

Abstract: In this paper, we design an algorithm by adaptive cubic regularization methods for solving multi-objective optimization problem. The regularization technique is based on the strategy of computing an ap-proximate global minimizer of a cubic overestimator of the objective function. The new method can effectively improve the iteration complexity. Theoretical analysis indicates the fact that the new method preserves the global convergence under some standard assumptions.

Keywords: Cubic regularization; Multi-objective optimization; Unconstrained optimization; Global conver-gence