NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT
NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT
摘要
This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.
This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.
基金
ThisworkwassupportedbyNationalNaturalScienceFoundationofChina(10071028)
参考文献12
-
1Wang G, Zhao Y, Li W. Some optimal control problems governed by elliptic variational inequalities with control and state constraint on the boundary. Journal of Optimization Theory and Applications, 2000, 106(3): 627-655.
-
2Wang G, Zhao Y, Li W. Optimal control governed by a semilinear elliptic differential equation. Nonlinear Analysis, 2001, 44:957-974.
-
3Barbu V. Analysis and Control of Nonlinear Infinite Dimensional Systems. New York: Academic Press,1993.
-
4Barbu V. Optimal Control of Variational Inequalities. Research Notes in Mathematics, 100. Pitman Publishing Limited, 1984.
-
5Bonnans F, Casas E. An extension of Pontryagin's principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities. SIAM J Control and Optimization, 1995, 33(1): 274-298.
-
6Casas E. Boundary Control Problems for Quasi-Linear Elliptic Equations: A Pontryagin's Principle. Appl Math Optim, 1996, 33:265-291.
-
7Casas E, Yong J. Maximum Principle for State-Constrained Optimal Control Problems Governed by Quasilinear Equations. Differential Integral Equation, 1995, 8(1): 1-18.
-
8Li X,Yong J. Optimal Control Theory for Infinite Dimensional Systems. Boston: Birhauser, 1995.
-
9He Zheng-Xu. State Constrained Control problems Governed By Variational Inequalities. SIAM J Control and Optimization, 1987, 25(5).
-
10Ioffe A D, Levin V I. SubdifferentiaI of convex functions. Trud Mosk Mat Obsc, 1972, 26:3-33.
-
1马晓娜.半B-(E,F)-凸函数的一些性质[J].宿州学院学报,2010,25(11):4-5.
-
2马晓娜.半B-(E,F)-凸约束单目标规划的最优性条件[J].四川理工学院学报（自然科学版）,2010,23(3):280-283. 被引量：1
-
3曾闽丽.一类涡流控制问题的新的预处理子[J].吉首大学学报（自然科学版）,2014,35(2):18-22.
-
4许英姿,岳书常,刘灿昌,刘露,荆栋.考虑非局部效应的碳纳米管磁时滞最优化控制[J].山东理工大学学报（自然科学版）,2015,29(4):6-10.
-
5马晓娜.关于半B-(E,F)-凸约束多目标规划的一个对偶定理[J].宜春学院学报,2014,36(9):29-31.
-
6袁俭.On the Uniqueness of the Positive Solution for a Semilinear Elliptic Problem with Critical Exponent[J].Chinese Quarterly Journal of Mathematics,1997,12(1):76-80.
-
7黄琳,李中.输出反馈二次型最优的可解性问题[J].中国科学（A辑）,1990,21(7):762-767. 被引量：7
-
8綦建刚,刘衍胜.Asymptotic Behavior of Nodal Solutions for Semilinear Elliptic Equationsin R^n[J].Chinese Quarterly Journal of Mathematics,1998,13(1):22-28.
-
9许鹏翔,陈锡庚.数学教学的最优化控制[J].广东第二师范学院学报,1989,20(3):97-101.
-
10刘冠琦,王玉文,史峻平.Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect[J].Applied Mathematics and Mechanics(English Edition),2009,30(11):1461-1468.
