124,744 research outputs found
Second order Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: L2 approach.
No full textHJB equations for the optimal control of differential equations with delays and state constraints, I: Regularity of viscosity solutions
No full textWe study a class of optimal control problems with state constraints, where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular, the so-called models with time to build; see [P. K. Asea and P. J. Zak, J. Econom. Dynam. Control, 23 (1999), pp. 1155-1175; M. Bambi, J. Econom. Dynam.. Control, 32 (2008), pp. 1015-1040; F. E. Kydland and E. C. Prescott, Econometrica, 50 (1982), pp. 1345-1370]. We embed the problem in a suitable Hilbert space H and consider the associated Hamilton-Jacobi-Bellman (HJB) equation. This kind of infinite dimensional HJB equation has not been previously studied and is difficult due to the presence of state constraints and the lack of smoothing properties of the state equation. Our main result on the regularity of solutions to such an HJB equation seems to be entirely new. More precisely, we prove that the value function is continuous in a sufficiently big open set of H, that it solves in the viscosity sense the associated HJB equation, and that it has continuous classical derivative in the direction of the "present." This regularity result is the starting point to define a feedback map in the classical sense, which gives rise to a candidate optimal feedback strategy. © 2010 Society for Industrial and Applied Mathematics
HJB Equations for the Optimal Control of DDE’s with State Constraints, I: Regularity of Viscosity Solutions
No full textHJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, II: Optimal Feedbacks and Approximations
No full textGoing Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
HJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, II: Verification and Optimal Feedbacks
No full textThis paper, which is the natural continuation of a paper by the same authors, studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. In the first paper the problem is embedded in a suitable Hilbert space H and the regularity of the associated Hamilton-Jacobi-Bellman (HJB) equation is studied. Therein the main result is that the value function V is a viscosity solution to the associated HJB equation and has continuous classical derivative in the direction of the "present". The goal of the present paper is to exploit this regularity result to prove a Verification Theorem and find optimal feedback controls for the problem. While it is easy to define a feedback control formally following the classical case, the proof of its existence and optimality is hard due to lack of full regularity of V and to the infinite dimensionality of the problem. The theory developed is applied to study economic problems of optimal growth for nonlinear time-tobuild models. In particular, we show the existence and uniqueness of optimal controls and their characterization as feedbacks
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