论文标题
非线性多目标优化问题的牛顿型近端梯度方法
A Newton-Type Proximal Gradient Method for Nonlinear Multi-objective Optimization Problems
论文作者
论文摘要
在本文中，为复合多目标优化问题而开发了全球收敛的牛顿型近端方法，其中每个目标函数可以表示为平滑函数和非平滑函数的总和。所提出的方法处理了无约束的凸多目标优化问题。此方法不含任何类型的先验选择参数或目标函数的订购信息。在所提出方法的每一次迭代中，都可以解决一个子问题以找到合适的下降方向。子问题使用每个平滑函数的二次近似。进行Armijo型线搜索以找到合适的步长。使用下降方向和步长生成序列。在某些温和的假设下，该方法的全球收敛是合理的。验证了所提出的方法，并使用一组问题与一些现有方法进行了比较。
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth function. The proposed method deals with unconstrained convex multi-objective optimization problems. This method is free from any kind of priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a suitable descent direction. The subproblem uses a quadratic approximation of each smooth function. An Armijo type line search is conducted to find a suitable step length. A sequence is generated using the descent direction and step length. The Global convergence of this method is justified under some mild assumptions. The proposed method is verified and compared with some existing methods using a set of problems.
