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  • Articles  (6)
  • Other Sources
  • Convergence  (3)
  • convergence  (3)
  • 1980-1984  (6)
  • Mathematics  (6)
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  • Articles  (6)
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  • 1
    Electronic Resource
    Electronic Resource
    Iterative methods for variational and complementarity problems (1982)
    Springer
    Mathematical programming 24 (1982), S. 284-313 
    Details
    ISSN: 1436-4646
    Keywords: Variational Inequality ; Complementarity ; Iterative Methods ; Convergence ; Traffic Equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585112
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Why use population entropy? It determines the rate of convergence (1982)
    Springer
    Journal of mathematical biology 13 (1982), S. 325-337 
    Details
    ISSN: 1432-1416
    Keywords: Population entropy ; Leslie model ; Markov chain ; Convergence ; Stable age distribution ; Ergodic theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary The population entropy introduced by Demetrius is shown to have a precise dynamical meaning as a measure of convergence rate to the stable age distribution. First the Leslie population model is transformed exactly into a Markov chain on a state space of age-classes. Next the dynamics of convergence from a nonequilibrium state to the stable state are analyzed. The results provide the first clear biological reason why entropy is a broadly useful population statistic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276067
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  • 3
    Electronic Resource
    Electronic Resource
    Primitivity and convergence to stability (1981)
    Springer
    Journal of mathematical biology 13 (1981), S. 241-246 
    Details
    ISSN: 1432-1416
    Keywords: Leslie matrix ; Index of primitivity ; Convergence ; Stable age distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An exact expression for the index of primitivity g of a Leslie matrix is obtained, which applies also to time-varying matrices which share an incidence matrix. Elapsed time (not time intervals) to primitivity is shown to depend only weakly on the discretization scheme used. A lower bound for speed of convergence to the stable (fixed or time-dependent as appropriate) state is given which depends sensitively on g.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275217
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  • 4
    Electronic Resource
    Electronic Resource
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 1 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 211-246 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; control constraints ; terminal equality constraints ; exact penalty function ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The presence of control constraints, because they are nondifferentiable in the space of control functions, makes it difficult to cope with terminal equality constraints in optimal control problems. Gradient-projection algorithms, for example, cannot be employed easily. These difficulties are overcome in this paper by employing an exact penalty function to handle the cost and terminal equality constraints and using the control constraints to define the space of permissible search directions in the search-direction subalgorithm. The search-direction subalgorithm is, therefore, more complex than the usual linear program employed in feasible-directions algorithms. The subalgorithm approximately solves a convex optimal control problem to determine the search direction; in the implementable version of the algorithm, the accuracy of the approximation is automatically increased to ensure convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934725
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  • 5
    Electronic Resource
    Electronic Resource
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 2 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 345-364 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; control constraints ; terminal equality constraints ; exact penalty functions ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Part 1 of this paper, implementable and conceptual versions of an algorithm for optimal control problems with control constraints and terminal equality constraints were presented. It was shown that anyL ∞ accumulation points of control sequences generated by the algorithms satisfy necessary conditions of optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithms always have accumulation points in the sense of control measure, and these accumulation points satisfy optimality conditions for the corresponding relaxed control problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934557
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  • 6
    Electronic Resource
    Electronic Resource
    Convergence of a strong variational algorithm for relaxed controls involving a class of hyperbolic systems (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 467-485 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; hyperbolic partial differential equations ; Darboux boundary conditions ; strong variational algorithm ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems involving linear hyperbolic partial differential equations with Darboux boundary conditions. A strong variational algorithm has been obtained for solving this class of optimal control problems in a previous paper by the third and the first authors. It was also shown that anyL ∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that the control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935327
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