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Sochastic maximum principle for forwardbackward stochastic control systems associated with Levy processes,”Chinese Annals ofMathematics,
, 2014
"... We study a stochastic optimal control problem where the controlled system is described by a forwardbackward stochastic differential equation driven by Lévy process. In order to get our main result of this paper, the maximum principle, we prove the continuity result depending on parameters about fu ..."
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Cited by 14 (3 self)
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We study a stochastic optimal control problem where the controlled system is described by a forwardbackward stochastic differential equation driven by Lévy process. In order to get our main result of this paper, the maximum principle, we prove the continuity result depending on parameters about fully coupled forwardbackward stochastic differential equations driven by Lévy process. Under some additional convexity conditions, the maximum principle is also proved to be sufficient. Finally, the result is applied to the linear quadratic problem.
First and second order optimality conditions for optimal control problems of state constrained integral equations
 Inria, May 2012, n o RR7961
"... Abstract This paper deals with optimal control problems of integral equations, with initialfinal and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and secondorder ..."
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Abstract This paper deals with optimal control problems of integral equations, with initialfinal and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and secondorder necessary conditions of optimality are obtained, as well as secondorder sufficient conditions.
An efficient hybrid pseudospectral method for solving optimal control of Volterra integral systems
, 2014
"... Abstract. In this paper, a new pseudospectral (PS) method is developed for solving optimal control problems governed by the nonlinear Volterra integral equation (VIE). The novel method is based upon approximating the state and control variables by the hybrid of block pulse functions and Legendre ..."
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Abstract. In this paper, a new pseudospectral (PS) method is developed for solving optimal control problems governed by the nonlinear Volterra integral equation (VIE). The novel method is based upon approximating the state and control variables by the hybrid of block pulse functions and Legendre polynomials. The properties of hybrid functions are presented. The numerical integration and collocation method is utilized to discretize the continuous optimal control problem and then the resulting largescale finitedimensional nonlinear programming (NLP) is solved by the existing welldeveloped algorithm in Mathematica software. A set of sufficient conditions is presented under which optimal solutions of discrete optimal control problems converge to the optimal solution of the continuous problem. The error bound of approximation is also given. Numerical experiments confirm efficiency of the proposed method especially for problems with nonsufficiently smooth solutions belonging to class C1 or C2.
9 9 IS R N IN R IA /R R 7 9 6 1 F R E
, 2012
"... ProjectTeams Commands First and second order optimality conditions for optimal control problems of state constrained integral equations J. Frédéric Bonnans, Constanza de la Vega, Xavier Dupuis ha l0 ..."
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ProjectTeams Commands First and second order optimality conditions for optimal control problems of state constrained integral equations J. Frédéric Bonnans, Constanza de la Vega, Xavier Dupuis ha l0