|
|
- 2017
一类锥约束变分不等式问题的间隙函数和误差界
|
Abstract:
鉴于间隙函数与误差界在优化方法中有重要的作用，特别地，误差界能刻画可行点和变分不等式解集之间的有效估计距离.利用像空间分析法，构造了带锥约束变分不等式的间隙函数.然后，利用此间隙函数，得到了带锥约束变分不等式的误差界.
The gap function and the error bound play an important role in optimization methods and the error bound, especially, can characterize the effective estimated distance between a feasible point and the solution set of variational inequalities. In this article, by using the image space analysis, gap functions for a class of variational inequalities with cone constraints are proposed. Moreover, error bounds, which provide an effective estimated distance between a feasible point and the solution set, for the variational inequalities are established via the gap functions
| [1] | HARKER P T, PANG J S. Finite-Dimensional Variational Inequalities and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms and Applications[J]. Math Program, 1990, 48: 161-220. DOI:10.1007/BF01582255 |
| [2] | CHARITHA C, DUTTA J. Regularized Gap Functions and Error Bounds for Vector Variational Inequalities[J]. Pac J Optim, 2011, 6(3): 497-510. |
| [3] | CHEN G Y, HUANG X X, YANG X Q. Vector Optimization: Set-Valued and Variational Analysis. Lecture Notes in Economics and Mathematical Systems[M]. Berlin: Springer, 2005: 541. |
| [4] | GERTH C, WEIDNER P. Nonconvex Separation Theorems and Some Applications in Vector Optimization[J]. J Optim Theory Appl, 1990, 67(2): 297-320. DOI:10.1007/BF00940478 |
| [5] | LUC D T. Theory of Vector Optimization[J]. Springer-Verlag, 2006, 319: 1-70. |
| [6] | FACCHINEI F, PANG J S. Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer Series in Operations Research[M]. New York(NY): Springer-Verlag, 2003. |
| [7] | FERRIS M C, PANG J S. Engineering and Economic Applications of Complementarity Problems[J]. SIAM Rev, 1997, 39(4): 669-713. DOI:10.1137/S0036144595285963 |
| [8] | MASTROENI G, PANICUCCI B, PASSACANTANDO M, et al. A Separation Approach to Vector Quasi-Equilibrium Problems: Saddle Point and Gap Function[J]. Taiwan J Math, 2009, 13(2): 657-673. |
| [9] | XU Y D. Nonlinear Separation Approach to Inverse Variational Inequalities[J]. Optimization, 2016, 28: 1-21. |
| [10] | GIANNESSI F. Constrained Optimization and Image Space Analysis. Vol.1. Separation of Sets and Optimality Conditions[J]. New York(NY): Springer, 2006, 48(2): 429-431. |
| [11] | LIGNOLA M B, MORGAN J. Convergence for Variational Inequalities and Generelized Variational Inequalities[J]. Atti Sem mat fis univ modena, 1997, 2: 377-388. |
| [12] | LI J, HUANG N J. Image Space Analysis for Variational Inequalities with Cone Constraints Applications to Traffic Equilibria[J]. Sci China Math, 2012, 55(4): 851-868. DOI:10.1007/s11425-011-4287-5 |
