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Bellman equation
About: Bellman equation is a research topic. Over the lifetime, 5884 publications have been published within this topic receiving 135589 citations.
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TL;DR: It is shown that the value function is the viscosity solution of the Hamilton–Jacobi–Bellman equation that leads to the optimal feedback control of the continuous casting process in the secondary cooling zone with water spray control.
Abstract: Using a semi-discrete model that describes the heat transfer of a continuous casting process of steel, this paper is addressed to an optimal control problem of the continuous casting process in the secondary cooling zone with water spray control. The approach is based on the Hamilton---Jacobi---Bellman equation satisfied by the value function. It is shown that the value function is the viscosity solution of the Hamilton---Jacobi---Bellman equation. The optimal feedback control is found numerically by solving the associated Hamilton---Jacobi---Bellman equation through a designed finite difference scheme. The validity of the optimality of the obtained control is experimented numerically through comparisons with different admissible controls. Detailed study of a low-carbon billet caster is presented.
41 citations
TL;DR: It turns out that a certain convexity of the equation plays a key role in the arguments of this paper.
Abstract: The paper is concerned with ergodic-type Bellman equations arising typically in linear (exponential) quadratic Gaussian control. We are interested in giving recurrence-transience criteria for associated optimal feedback diffusions in terms of qualitative properties of solutions to the Bellman equation. To establish such criteria, we propose a new approach which is based on the Lyapunov method. It turns out that a certain convexity of the equation plays a key role in our arguments.
41 citations
TL;DR: This work focuses on numerical methods for finding optimal investment, dividend payment, and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections.
41 citations
TL;DR: In this article, the authors considered a general optimal control problem in which the constraints depend on a parameter and the resulting value function, and a formula for the generalized gradient of V was proven and then used to obtain results on stability and controllability of the problem.
Abstract: We consider a general optimal control problem in which the constraints depend on a parameter $\alpha $, and the resulting value function $V(\alpha )$. A formula for the generalized gradient of V is proven and then used to obtain results on stability and controllability of the problem. A special study is made of the time-optimal control problem, one consequence of which is a new criterion assuring local null-controllability of the system and continuity of the minimal time function at the origin.
41 citations
TL;DR: In this paper, a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic MILO problems with recourse is introduced, which highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework.
Abstract: We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.
41 citations