POINTWISE SECOND-ORDER NECESSARY CONDITIONS FOR STOCHASTIC OPTIMAL CONTROLS, PART I: THE CASE OF CONVEX CONTROL CONSTRAINT

被引：29
|
作者：
Zhang, Haisen [1 ,2 ]
Zhang, Xu [2 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
[2] Sichuan Univ, Sch Math, Chengdu 610064, Sichuan Provinc, Peoples R China
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2015年 / 53卷 / 04期
关键词：
stochastic optimal control; malliavin calculus; pointwise second-order necessary condition; variational equation; adjoint equation; MAXIMUM PRINCIPLE; HIGH-ORDER; REGULARITY;
D O I：
10.1137/14098627X
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper is the first part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region is assumed to be convex. Under some assumptions in terms of the Malliavin calculus, we establish the desired necessary conditions for stochastic singular optimal controls in the classical sense.
引用
收藏
页码：2267 / 2296
页数：30
相关论文
共 50 条
  • [21] Second-Order Necessary Conditions for Optimal Control Problems with Endpoints-Constraints and Convex Control-Constraints
    Li, Deng
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2022, 60 (05) : 2737 - 2758
  • [22] SECOND-ORDER NECESSARY CONDITIONS FOR OPTIMAL CONTROL OF SEMILINEAR ELLIPTIC EQUATIONS WITH LEADING TERM CONTAINING CONTROLS
    Lou, Hongwei
    Yong, Jiongmin
    MATHEMATICAL CONTROL AND RELATED FIELDS, 2018, 8 (01) : 57 - 88
  • [23] First and Second Order Necessary Conditions for Stochastic Optimal Control Problems
    J. Frédéric Bonnans
    Francisco J. Silva
    Applied Mathematics & Optimization, 2012, 65 : 403 - 439
  • [24] First and Second Order Necessary Conditions for Stochastic Optimal Control Problems
    Bonnans, J. Frederic
    Silva, Francisco J.
    APPLIED MATHEMATICS AND OPTIMIZATION, 2012, 65 (03): : 403 - 439
  • [25] Second-Order Necessary Optimality Conditions for a Discrete Optimal Control Problem
    Toan, N. T.
    Ansari, Q. H.
    Yao, J-C.
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 165 (03) : 812 - 836
  • [26] Second-Order Necessary Optimality Conditions in Optimal Impulsive Control Problems
    A. V. Arutyunov
    D. Yu. Karamzin
    F. L. Pereira
    N. Yu. Chernikova
    Differential Equations, 2018, 54 : 1083 - 1101
  • [27] Second-order necessary optimality conditions for a discrete optimal control problem
    Mingaleeva, Z. T.
    Shvartsman, I. A.
    DIFFERENTIAL EQUATIONS, 2014, 50 (12) : 1643 - 1649
  • [28] Second-order necessary optimality conditions for a discrete optimal control problem
    Z. T. Mingaleeva
    I. A. Shvartsman
    Differential Equations, 2014, 50 : 1643 - 1649
  • [29] Second-Order Necessary Optimality Conditions for a Discrete Optimal Control Problem
    N. T. Toan
    Q. H. Ansari
    J.-C. Yao
    Journal of Optimization Theory and Applications, 2015, 165 : 812 - 836
  • [30] Second-Order Necessary Optimality Conditions in Optimal Impulsive Control Problems
    Arutyunov, A. V.
    Karamzin, D. Yu.
    Pereira, F. L.
    Chernikova, N. Yu.
    DIFFERENTIAL EQUATIONS, 2018, 54 (08) : 1083 - 1101
12345