多目标优化非单调线性加权牛顿算法

Nonmonotone Linear Weighted Newton Algorithm for Multi-Objective Optimization

本文提出了一种求解多目标优化问题的非单调线性加权牛顿算法。在目标函数有下界且梯度Lipschitz连续的条件下证明了算法的全局收敛性。在目标函数满足二次连续可微且局部强凸的条件下,证明了该算法具有局部超线性收敛速度。数值实验结果表明,相比于单调线性加权牛顿算法,该算法能够更加高效地求解多目标优化问题。

This paper introduces a nonmonotone linear weighted Newton algorithm for solving multi-objective optimization problems. It is shown that the algorithm achieves global convergence under the assumption of a lower bound on the objective function and a Lipschitz continuous gradient. Furthermore, under the conditions of quadratic continuous differentiability and local strong convexity, the algorithm demonstrates local superlinear convergence. Numerical experiments demonstrate that this algorithm outperforms the monotone linear weighted Newton algorithm in efficiently solving multi-objective optimization problems.