A limited memory Quasi-Newton approach for multi-objective optimization
本文首次提出一种有限记忆拟牛顿方法求解无约束多目标优化问题，适用于大规模场景，通过近似目标函数Hessian矩阵的凸组合，并采用Wolfe线搜索，证明了非凸情形下的良定义性及强凸情形下的全局与R-线性收敛性，实验表明该方法高效且优于现有方法。
Abstract In this paper, we deal with the class of unconstrained multi-objective optimization problems. In this setting we introduce, for the first time in the literature, a Limited Memory Quasi-Newton type method, which is well suited especially in large scale scenarios. The proposed algorithm approximates, through a suitable positive definite matrix, the convex combination of the Hessian matrices of the objectives; the update formula for the approximation matrix can be seen as an extension of the one used in the popular L-BFGS method for scalar optimization. Equipped with a Wolfe type line search, the considered method is proved to be well defined even in the nonconvex case. Furthermore, for twice continuously differentiable strongly convex problems, we state global and R-linear convergence to Pareto optimality of the sequence of generated points. The performance of the new algorithm is empirically assessed by a thorough computational comparison with state-of-the-art Newton and Quasi-Newton approaches from the multi-objective optimization literature. The results of the experiments highlight that the proposed approach is generally efficient and effective, outperforming the competitors in most settings. Moreover, the use of the limited memory method results to be beneficial within a global optimization framework for Pareto front approximation.