Subgradients of the Value Function in a Parametric Convex Optimal Control Problem
Motivated by our recent works on the optimal value function in parametric optimal control problems under linear state equations, in this paper we study of the first-order behavior of the value function of a parametric convex optimal control problem with a convex cost function and linear state equati...
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| Veröffentlicht in: | Journal of optimization theory and applications 2016-07, Vol.170 (1), p.43-64 |
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| container_title | Journal of optimization theory and applications |
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| creator | Thuy, Le Quang Toan, Nguyen Thi |
| description | Motivated by our recent works on the optimal value function in parametric optimal control problems under linear state equations, in this paper we study of the first-order behavior of the value function of a parametric convex optimal control problem with a convex cost function and linear state equations. By establishing an abstract result on the subdifferential of the value function to a parametric convex mathematical programming problem, we derive a formula for computing the subdifferential and the singular subdifferential of the value function to a parametric convex optimal control problem. By virtue of the convexity, several assumptions used in the above papers, like the existence of a local upper Lipschitzian selection of the solution map, as well as the V-inner semicontinuity of the solution map, are no longer needed. |
| doi_str_mv | 10.1007/s10957-016-0921-2 |
| format | Article |
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By establishing an abstract result on the subdifferential of the value function to a parametric convex mathematical programming problem, we derive a formula for computing the subdifferential and the singular subdifferential of the value function to a parametric convex optimal control problem. 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By establishing an abstract result on the subdifferential of the value function to a parametric convex mathematical programming problem, we derive a formula for computing the subdifferential and the singular subdifferential of the value function to a parametric convex optimal control problem. 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| subjects | Applications of Mathematics Calculus of Variations and Optimal Control Optimization Computation Control theory Differential equations Engineering Equations of state Formulas (mathematics) Mathematical analysis Mathematical functions Mathematical models Mathematical programming Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimal control Optimization Studies Theory of Computation |
| title | Subgradients of the Value Function in a Parametric Convex Optimal Control Problem |
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