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  • 1
    Electronic Resource
    Electronic Resource
    On the average cost optimality equation and the structure of optimal policies for partially observable Markov decision processes (1991)
    Springer
    Annals of operations research 29 (1991), S. 439-469 
    Details
    ISSN: 1572-9338
    Keywords: Optimal control ; Markov chains ; partial observability ; average cost ; optimality equation ; structured optimal policies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider partially observable Markov decision processes with finite or countably infinite (core) state and observation spaces and finite action set. Following a standard approach, an equivalent completely observed problem is formulated, with the same finite action set but with anuncountable state space, namely the space of probability distributions on the original core state space. By developing a suitable theoretical framework, it is shown that some characteristics induced in the original problem due to the countability of the spaces involved are reflected onto the equivalent problem. Sufficient conditions are then derived for solutions to the average cost optimality equation to exist. We illustrate these results in the context of machine replacement problems. Structural properties for average cost optimal policies are obtained for a two state replacement problem; these are similar to results available for discount optimal policies. The set of assumptions used compares favorably to others currently available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02283610
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  • 2
    Electronic Resource
    Electronic Resource
    A Technique for Stochastic Control Problems with Unbounded Control Set (1999)
    Springer
    Journal of theoretical probability 12 (1999), S. 255-270 
    Details
    ISSN: 1572-9230
    Keywords: Optimal control ; stochastic differential equations ; convergence in law ; unbounded control set ; suboptimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This device yields a natural sequence of suboptimal controls for the original problem. By this we mean a sequence of controls for which the payoff functions approach the value function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021761030407
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  • 3
    Electronic Resource
    Electronic Resource
    Opticon: An algorithm for the optimal control of nonlinear stochastic models (1992)
    Springer
    Annals of operations research 37 (1992), S. 375-401 
    Details
    ISSN: 1572-9338
    Keywords: Optimal control ; stochastic control ; dynamic systems ; nonlinear systems ; control algorithm ; optimal economic policies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we describe the algorithm OPTCON which has been developed for the optimal control of nonlinear stochastic models. It can be applied to obtain approximate numerical solutions of control problems where the objective function is quadratic and the dynamic system is nonlinear. In addition to the usual additive uncertainty, some or all of the parameters of the model may be stochastic variables. The optimal values of the control variables are computed in an iterative fashion: First, the time-invariant nonlinear system is linearized around a reference path and approximated by a time-varying linear system. Second, this new problem is solved by applying Bellman's principle of optimality. The resulting feedback equations are used to project expected optimal state and control variables. These projections then serve as a new reference path, and the two steps are repeated until convergence is reached. The algorithm has been implemented in the statistical programming system GAUSS. We derive some mathematical results needed for the algorithm and give an overview of the structure of OPTCON. Moreover, we report on some tentative applications of OPTCON to two small macroeconometric models for Austria.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02071066
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  • 4
    Electronic Resource
    Electronic Resource
    Exploitation of natural resources and pollution (1994)
    Springer
    Annals of operations research 54 (1994), S. 237-262 
    Details
    ISSN: 1572-9338
    Keywords: Optimal control ; differential games ; environmental policy ; JEL C61 ; C73 ; Q28
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper provides some differential game models of natural resource exploitation when environmental pollution takes place. The “classical” approach to determine optimal harvest rates of renewable resources utilizes Optimal Control models, i.e. there is either a monopolistic market structure or there is pure competition. In case of pollution, however, all agents can be put together, forming the groups of the resource harvesters on one side and of polluters on the other side. So differential games can be used to analyze environmental problems. The models introduced in this paper are put together in order to showdifferent problems that can all be analyzed using differential games.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02031736
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  • 5
    Electronic Resource
    Electronic Resource
    Optimal budgetary and monetary policies under uncertainty: A stochastic control approach (1995)
    Springer
    Annals of operations research 58 (1995), S. 379-402 
    Details
    ISSN: 1572-9338
    Keywords: Optimal control ; stochastic control ; dynamic systems ; economics ; public-sector applications ; optimization ; budgetary policies ; monetary policy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we determine optimal budgetary and monetary policies for Austria using a small macroeconometric model. We use a Keynesian model of the Austrian economy, called FINPOL1, estimated by ordinary least squares, which relates the main objective variables of Austrian economic policies, such as the growth rate of real gross domestic product, the rate of unemployment, the rate of inflation, the balance of payments, and the ratio of the federal budget deficit to GDP, to fiscal and monetary policy instruments, namely expenditures and revenues of the federal budget and money supply. Optimal fiscal and monetary policies are calculated for the model under a quadratic objective function using the algorithm OPTCON for the optimum control of nonlinear stochastic dynamic systems. Several control experiments are performed in order to assess the influence of different kinds of uncertainty on optimal budgetary and monetary policies. Apart from deterministic optimization runs, different assumptions about parameter uncertainties are introduced; the results of these different stochastic optimum control experiments are compared and interpreted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02038862
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  • 6
    Electronic Resource
    Electronic Resource
    Optimal pollution control, irreversibilities, and the value of future information (1994)
    Springer
    Annals of operations research 54 (1994), S. 217-235 
    Details
    ISSN: 1572-9338
    Keywords: Optimal control ; growth paths ; exhaustible resources ; JEL C61 ; O41 ; Q23
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper focuses on the issue of optimal pollution control when either pollution itself is irreversible or when some characteristic of the environmental resource is irreversibly destroyed in the course of growing pollution. It is shown that exhausting the assimilative capacity through too heavy pollution is never optimal unless the rate of social time preference is sufficiently high. The paper also investigates the case that decisions about irreversible developments have to be made under uncertainty today when the decision maker faces the prospect of better information about the irreversible damage at some future point in time. A non-negative quasi-option value is shown to exist as in the Arrow-Fisher-Henry model that relates to natural resource deletion by projects of industrial development.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02031735
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  • 7
    Electronic Resource
    Electronic Resource
    Adaptive finite element for semi-linear convection–diffusion problems (1997)
    Springer
    Advances in computational mathematics 7 (1997), S. 235-259 
    Details
    ISSN: 1572-9044
    Keywords: numerical analysis ; nonlinear ; elliptic equations ; finite element ; error estimates ; 35K55 ; 65N15 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this article a strategy of adaptive finite element for semi-linear problems, based on minimizing a residual-type estimator, is reported. We get an a posteriori error estimate which is asymptotically exact when the mesh size h tends to zero. By considering a model problem, the quality of this estimator is checked. It is numerically shown that without constraint on the mesh size h, the efficiency of the a posteriori error estimate can fail dramatically. This phenomenon is analysed and an algorithm which equidistributes the local estimators under the constraint h ⩽ h max is proposed. This algorithm allows to improve the computed solution for semi-linear convection–diffusion problems, and can be used for stabilizing the Lagrange finite element method for linear convection–diffusion problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018946919497
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  • 8
    Electronic Resource
    Electronic Resource
    An explicit norm representation for the analysis of multilevel methods (1998)
    Springer
    Advances in computational mathematics 9 (1998), S. 311-335 
    Details
    ISSN: 1572-9044
    Keywords: symmetric variational problems ; additive Schwarz schemes ; multilevel methods ; sparse grids ; approximation spaces ; non-nested finite element spaces ; 65J10 ; 65N12 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the present paper we develop a representation of a norm frequently used in the analysis of multilevel methods. This allows us to examine the convergence of additive Schwarz schemes also in the case of non-nested subspaces. We demonstrate the usefulness of the given norm representation by studying in detail the stability of sparse grid splittings due to Griebel and Oswald, which turns out to be a special case of our unified theory. Further applications concerning approximation spaces and non-nested finite element spaces are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018949809444
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  • 9
    Electronic Resource
    Electronic Resource
    Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution (1993)
    Springer
    Advances in computational mathematics 1 (1993), S. 259-335 
    Details
    ISSN: 1572-9044
    Keywords: Periodic pseudodifferential equations ; pre-wavelets ; biorthogonal wavelets ; generalized Petrov-Galerkin schemes ; wavelet representation ; atomic decomposition ; Calderón-Zygmund operators ; matrix compression ; error analysis ; 65F35 ; 65J10 ; 65N30 ; 65N35 ; 65R20 ; 47A20 ; 47G30 ; 45P05 ; 41A25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This is the second part of two papers which are concerned with generalized Petrov-Galerkin schemes for elliptic periodic pseudodifferential equations in ℝ n . This setting covers classical Galerkin methods, collocation, and quasi-interpolation. The numerical methods are based on a general framework of multiresolution analysis, i.e. of sequences of nested spaces which are generated by refinable functions. In this part, we analyse compression techniques for the resulting stiffness matrices relative to wavelet-type bases. We will show that, although these stiffness matrices are generally not sparse, the order of the overall computational work which is needed to realize a certain accuracy is of the formO(N(logN) b ), whereN is the number of unknowns andb ≥ 0 is some real number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02072014
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  • 10
    Electronic Resource
    Electronic Resource
    A quasi-wavelet algorithm for second kind boundary integral equations (1999)
    Springer
    Advances in computational mathematics 11 (1999), S. 355-375 
    Details
    ISSN: 1572-9044
    Keywords: periodic quasi-wavelet ; integral equation ; multiscale ; 45G10 ; 65F10 ; 65J15 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In solving integral equations with a logarithmic kernel, we combine the Galerkin approximation with periodic quasi-wavelet (PQW) [4]. We develop an algorithm for solving the integral equations with only O(N log N) arithmetic operations, where N is the number of knots. We also prove that the Galerkin approximation has a polynomial rate of convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018992413504
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