JIANG Jinxi,LIU Wenbin,JIN Yan.Existence of solution for an optimal control problem governed by semi-linear elliptic variational inequality[J].Journal of Yanbian University,2014,40(04):295-298.
一个半线性椭圆型变分不等式约束下的最优控制问题解的存在性
- Title:
- Existence of solution for an optimal control problem governed by semi-linear elliptic variational inequality
- 分类号:
- O177.92
- 文献标志码:
- A
- 摘要:
- 目标泛函相对于状态函数不可微的情形下,利用分解法和引入罚微分方程式等过程,研究了一个半线性椭圆型变分不等式最优控制问题,并证明了其解的存在性.
- Abstract:
- In this paper, an optimal control problem governed by semi-linear elliptic variational inequality is studied by means of decomposition and process of introducing a penalty differential equation, and the existence of solution is proved, where the objective function is not differential with respect to the state function.
参考文献/References:
[1] Bermudez A, Saguez C. Optimal control of a sigorrini problem[J]. SIAM Journal on Control and Optimization, 1987,25(3):576-587.
[2] Bermudez A, Saguez C. Optimal control of variational inequalities[J]. Control and Cybernetics, 1985,14(1/3):9-30.
[3] He Zhengxu. State constramed control problems governed by variational inequalities[J]. SIAM Journal on Control and Optimization, 1987,25(5):1119-1144.
[4] 张石生,向淑文.一类型变分不等式解的存在性唯一性问题及其对力学中的Signorini问题的应用[J].应用数学与力学,1991,12(5):401-406.
[5] 陈学华.带不变凸的非光滑约束分式最优控制问题的对偶[J].苏州大学学报:自然科学版,2001,17(3):27-34.
[6] David Adams R, Suzanne Tenhard. Optimal shape design subject to ellptic viriational inequalities[J]. Applied Mathematics and Optimization, 2003,47(1):79-95.
[7] Hintermuller M, Laurain A. Optimal shape design subject to ellptic variational inequalities[J]. SIAM Journal on Control and Optimization, 2011,49(3):1015-1047.
[8] Gunzburger M D, Manservis S. Analisis and approximation of the velocity tracking problem for navier-stokes flows with distributed control[J]. SIAM Journal on Numerical Analysis, 2000,37(5):1481-1512.
[9] Gunzburger M D, Manservis S. The velocity traching problem for navier-stokes flows with boundary control[J]. SIAM Journal on Numerical Analysis, 2001,39(2):594-634.
[10] Arada N, Raymond J P. Optimal control problems with mixed control-state constraints[J]. SIAM Journal on Control and Optimization, 2000,39(5):1391-1407.
[11] Chen Qihong, Chu Delin, Roger Tan C E. Optimal contrrol of obstacle for quasi-linear elliptic variational problems[J]. SIAM Journal on Control and Optimization, 2005,44(3):1067-1080.
[12] Lou Hongwei. An optimal control problem governed by quasi-linear variational inequalities[J]. SIAM Journal on Control and Optimization, 2002,41(4):1229-1253.
相似文献/References:
[1]姜今锡,金艳,金元峰.一个半线性椭圆型变分不等式最优控制问题的近似解序列的收敛性[J].延边大学学报(自然科学版),2016,42(02):103.
JIANG Jinxi,JIN Yan,JIN Yuanfeng.The convergence of the approximate solution sequence of optimal control problem for a semi-linear elliptic variational inequality[J].Journal of Yanbian University,2016,42(04):103.
备注/Memo
收稿日期: 2014-07-08作者简介: 姜今锡(1959—),男,博士,教授,研究方向为概率统计、最优化理论.