American Institute of Mathematical Sciences

Advanced
November  2010, 14(4): 1581-1599. doi: 10.3934/dcdsb.2010.14.1581

A second-order maximum principle for singular optimal stochastic controls

Shanjian Tang 1,

1. 

Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received  March 2009 Revised  November 2009 Published  August 2010

A singular optimal stochastic control problem is studied. A second-order maximum principle is presented. The second-order adjoint processes are involved, though the diffusion of the control system is control independent. The range theorem of vector-valued measures is used to prove the maximum principle. Examples are given to illustrate the applications.
Keywords: first and second adjoint processes, vector-valued measure theory., second-order maximum principle, Singular optimal stochastic control, spike variation.
Mathematics Subject Classification: Primary: 93E20; Secondary: 60H30, 60G3.
Citation: Shanjian Tang. A second-order maximum principle for singular optimal stochastic controls. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1581-1599. doi: 10.3934/dcdsb.2010.14.1581
[1]

Hancheng Guo, Jie Xiong. A second-order stochastic maximum principle for generalized mean-field singular control problem. Mathematical Control & Related Fields, 2018, 8 (2) : 451-473. doi: 10.3934/mcrf.2018018
[2]

Doyoon Kim, Seungjin Ryu. The weak maximum principle for second-order elliptic and parabolic conormal derivative problems. Communications on Pure & Applied Analysis, 2020, 19 (1) : 493-510. doi: 10.3934/cpaa.2020024
[3]

Leonardo Colombo, David Martín de Diego. Second-order variational problems on Lie groupoids and optimal control applications. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6023-6064. doi: 10.3934/dcds.2016064
[4]

Bernd Kawohl, Vasilii Kurta. A Liouville comparison principle for solutions of singular quasilinear elliptic second-order partial differential inequalities. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1747-1762. doi: 10.3934/cpaa.2011.10.1747
[5]

Rui Li, Yingjing Shi. Finite-time optimal consensus control for second-order multi-agent systems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 929-943. doi: 10.3934/jimo.2014.10.929
[6]

Hongwei Lou, Jiongmin Yong. Second-order necessary conditions for optimal control of semilinear elliptic equations with leading term containing controls. Mathematical Control & Related Fields, 2018, 8 (1) : 57-88. doi: 10.3934/mcrf.2018003
[7]

Hongwei Lou. Second-order necessary/sufficient conditions for optimal control problems in the absence of linear structure. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1445-1464. doi: 10.3934/dcdsb.2010.14.1445
[8]

Leonardo Colombo. Second-order constrained variational problems on Lie algebroids: Applications to Optimal Control. Journal of Geometric Mechanics, 2017, 9 (1) : 1-45. doi: 10.3934/jgm.2017001
[9]

Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195
[10]

Gábor Kiss, Bernd Krauskopf. Stability implications of delay distribution for first-order and second-order systems. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 327-345. doi: 10.3934/dcdsb.2010.13.327
[11]

Qilin Wang, Shengji Li, Kok Lay Teo. Continuity of second-order adjacent derivatives for weak perturbation maps in vector optimization. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 417-433. doi: 10.3934/naco.2011.1.417
[12]

Qiong Meng, X. H. Tang. Multiple solutions of second-order ordinary differential equation via Morse theory. Communications on Pure & Applied Analysis, 2012, 11 (3) : 945-958. doi: 10.3934/cpaa.2012.11.945
[13]

Kyeong-Hun Kim, Kijung Lee. A weighted $L_p$-theory for second-order parabolic and elliptic partial differential systems on a half space. Communications on Pure & Applied Analysis, 2016, 15 (3) : 761-794. doi: 10.3934/cpaa.2016.15.761
[14]

José F. Cariñena, Javier de Lucas Araujo. Superposition rules and second-order Riccati equations. Journal of Geometric Mechanics, 2011, 3 (1) : 1-22. doi: 10.3934/jgm.2011.3.1
[15]

Eugenii Shustin, Emilia Fridman, Leonid Fridman. Oscillations in a second-order discontinuous system with delay. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 339-358. doi: 10.3934/dcds.2003.9.339
[16]

Lassi Roininen, Petteri Piiroinen, Markku Lehtinen. Constructing continuous stationary covariances as limits of the second-order stochastic difference equations. Inverse Problems & Imaging, 2013, 7 (2) : 611-647. doi: 10.3934/ipi.2013.7.611
[17]

Li Chu, Bo Wang, Jie Zhang, Hong-Wei Zhang. Convergence analysis of a smoothing SAA method for a stochastic mathematical program with second-order cone complementarity constraints. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020050
[18]

Liu Yang, Xiaojiao Tong, Yao Xiong, Feifei Shen. A smoothing SAA algorithm for a portfolio choice model based on second-order stochastic dominance measures. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1171-1185. doi: 10.3934/jimo.2018198
[19]

Lucas Bonifacius, Ira Neitzel. Second order optimality conditions for optimal control of quasilinear parabolic equations. Mathematical Control & Related Fields, 2018, 8 (1) : 1-34. doi: 10.3934/mcrf.2018001
[20]

Hans Josef Pesch. Carathéodory's royal road of the calculus of variations: Missed exits to the maximum principle of optimal control theory. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 161-173. doi: 10.3934/naco.2013.3.161

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (105)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences