非光滑多目标优化问题的光滑化刻画

The Smoothing Methods for Nonsmooth Multiobjective Optimization Problems

文章研究了非光滑多目标优化问题的光滑化方法.首先针对含有特殊结构的非光滑多目标优化问题给出了相应的光滑化模型,并在线性标量化方法的基础上建立了非光滑优化问题的弱有效解、有效解以及真有效解与光滑多目标优化问题的近似弱有效解、近似有效解以及近似真有效解之间的关系.此外,针对一般的非光滑多目标优化问题建立了一类光滑多目标优化模型,给出了非光滑优化问题的解集刻画.最后,通过光滑化方法在l1惩罚问题中的应用说明结果的合理性.

This is a research paper on smoothing methods for nonsmooth multiobjective optimization problems.Firstly,we discuss the corresponding smooth model for nonsmooth multiobjective optimization problems with special structures.Based on the linear scalarization method,we establish the relationship between the weakly efficient solution,the efficient solution and the properly efficient solution of the nonsmooth optimization problem and the approximate weakly efficient solution,the approximate efficient solution and the approximate properly efficient solution of the smooth multiobjective optimization problem.In addition,for general nonsmooth multiobjective optimization problems,a class of smooth multiobjective optimization model is established,which presents the solution set characterization of nonsmooth optimization problems.Finally,we give an example to illustrate the rationality of our results.