Inverse problems for vector variational and vector quasi-variational inequalities

被引:0
作者
Hebestreit N. [1 ]
Khan A.A. [2 ]
Tammer C. [1 ]
机构
[1] Department of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle (Saale)
[2] Center for Applied and Computational Mathematics, Rochester Institute of Technology, Rochester, NY
来源
Applied Set-Valued Analysis and Optimization | 2019年 / 1卷 / 03期
关键词
Inverse problem; Regularization; Vector quasi-variational inequality; Vector-variational inequality;
D O I
10.23952/asvao.1.2019.3.05
中图分类号
学科分类号
摘要
In this paper, we focus on an inverse problem of parameter identification in vector variational and vector quasi-variational inequalities. Especially, we develop an abstract regularization approach that permits a stable identification of the parameters in the considered variational problems. We give existence results for the regularized output least-square-based optimization problem and provide an application of our results to the Markowitz portfolio problem. © 2019 Applied Set-Valued Analysis and Optimization.
引用
收藏
页码:307 / 317
页数:10
相关论文
共 27 条
  • [1] Ansari Q. H., Kobis E., Yao J.-C., Vector Variational Inequalities and Vector Optimization, (2018)
  • [2] Bensoussan A., Lions J. L., Nouvelle formulation de problemes de controle impulsionenel et applications, C. R. Acad. Sci. Paris, 276, pp. 1189-1192, (1973)
  • [3] Chen G.-Y., Yang X.-Q., The vector complementary problem and its equivalences with the weak minimal element in ordered spaces, J. Math. Anal. Appl, 153, pp. 136-158, (1990)
  • [4] Crossen E., Gockenbach M. S., Jadamba B., Khan A. A., Winkler B., An equation error approach for the elasticity imaging inverse problem for predicting tumor location, Comput. Math. Appl, 67, pp. 122-135, (2014)
  • [5] Chen G., Huang X.X., Yang X., Vector Optimization: Set-Valued and Variational Analysis, (2005)
  • [6] Ehrgott M., Klamroth K., Schwehm C., An MCDM approach to portfolio optimization, European J. Oper. Res, 155, pp. 752-770, (2004)
  • [7] Elster R., Hebestreit N., Khan A. A., Tammer C., Inverse generalized vector variational inequalities with respect to variable domination structures and applications to vector approximation problems, Appl. Anal. Optim, 3, pp. 341-372, (2018)
  • [8] Giannessi F., Theorem of the alternative, quadratic programs, and complementary problems, Variational Inequalities and Complementarity Problems, (1980)
  • [9] Gockenbach M. S., Jadamba B., Khan A. A., Equation error approach for elliptic inverse problems with an application to the identification of Lame parameters, Inverse Probl. Sci. Eng, 16, pp. 349-367, (2008)
  • [10] Gopfert A., Tammer C., Zalinescu C., Variational Methods in Partially Ordered Spaces, (2003)