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  • 1
    Electronic Resource
    Electronic Resource
    On unbounded solutions of Bellman's equation associated with optimal switching control problems with state constraints (1995)
    Springer
    Applied mathematics & optimization 31 (1995), S. 1-17 
    Details
    ISSN: 1432-0606
    Keywords: Bellman equation ; Hamilton-Jacobi equation ; Quasi-variational inequality ; Viscosity solution ; Unbounded solutions ; Optimal switching ; Optimal control ; State constraints ; Production engineering ; 49C05 ; 49C20 ; 49B10 ; 49A36
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study a quasi-variational inequality system with unbounded solutions. It represents the Bellman equation associated with an optimal switching control problem with state constraints arising from production engineering. We show that the optimal cost is the unique viscosity solution of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182554
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Fast Computational Procedure for Solving Multi-Item Single-Machine Lot Scheduling Optimization Problems (1997)
    Springer
    Journal of optimization theory and applications 93 (1997), S. 491-515 
    Details
    ISSN: 1573-2878
    Keywords: Production schedule ; scheduling problems ; quasivariational inequalities ; Bellman equation ; numerical solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we deal with the numerical solution of the optimal scheduling problem in a multi-item single machine. We develop a method of discretization and a computational procedure which allows us to compute the solution in a short time and with a precision of order k, where k is the discretization size. In our method, the nodes of the triangulation mesh are joined by segments of trajectories of the original system. This special feature allows us to obtain precision of order k, which is in general impossible to achieve by usual methods. Also, we develop a highly efficient algorithm which converges in a finite number of steps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022682711077
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Relaxation of Minimax Optimal Control Problems with Infinite Horizon (1999)
    Springer
    Journal of optimization theory and applications 101 (1999), S. 285-306 
    Details
    ISSN: 1573-2878
    Keywords: Minimax optimal control problems ; infinite-horizon problems ; relaxation ; weak compactness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A minimax optimal control problem with infinite horizon is studied. We analyze a relaxation of the controls, which allows us to consider a generalization of the original problem that not only has existence of an optimal control but also enables us to approximate the infinite-horizon problem with a sequence of finite-horizon problems. We give a set of conditions that are sufficient to solve directly, without relaxation, the infinite-horizon problem as the limit of finite-horizon problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021785409703
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Fast solution of the obstacle problem (1993)
    Springer
    Journal of optimization theory and applications 79 (1993), S. 183-195 
    Details
    ISSN: 1573-2878
    Keywords: Obstacle problem ; fast algorithms ; numerical solutions ; variational inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is to present a fast algorithm for the numerical solution of the one-dimensional obstacle problem. It is proven that the algorithm converges in a finite number of steps; application examples showing its efficiency are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00941893
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Optimization of heat flux in domains with temperature constraints (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 245-256 
    Details
    ISSN: 1573-2878
    Keywords: Steady-state Stefan problem ; mixed elliptic differential problem ; constraint optimization problems ; heat flux optimization problem ; Lagrange multipliers theory ; explicit solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we deal with a heat flux optimization problem. We maximize the heat output flow on a portion of a domain's boundary, while on the other portion the distribution of the temperature is fixed. The maximization is carried out under the condition that there are no phase changes. The problem is solved using a convex-functional optimization technique, on Banach spaces, within restricted sets, yielding existence and uniqueness of the solution. The explicit form of the solution and the corresponding Lagrange multipliers associated to the problem are also given. In addition, other optimization problems related to the maximum bound of the heat flux with no phase change are solved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01102344
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    Paper (German National Licenses)
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