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  • reduced Hessian methods  (2)
  • Key words: constrained optimization – interior point method – large-scale optimization – nonlinear programming – primal method – primal-dual method – SQP iteration – barrier method – trust region method Mathematics Subject Classification (1991): 20E28, 20G40, 20C20  (1)
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  • 1
    Digitale Medien
    Digitale Medien
    An analysis of reduced Hessian methods for constrained optimization (1990)
    Springer
    Mathematical programming 49 (1990), S. 285-323 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Constrained optimization ; reduced Hessian methods ; quasi-Newton methods ; successive quadratic programming ; nonlinear programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We study the convergence properties of reduced Hessian successive quadratic programming for equality constrained optimization. The method uses a backtracking line search, and updates an approximation to the reduced Hessian of the Lagrangian by means of the BFGS formula. Two merit functions are considered for the line search: theℓ 1 function and the Fletcher exact penalty function. We give conditions under which local and superlinear convergence is obtained, and also prove a global convergence result. The analysis allows the initial reduced Hessian approximation to be any positive definite matrix, and does not assume that the iterates converge, or that the matrices are bounded. The effects of a second order correction step, a watchdog procedure and of the choice of null space basis are considered. This work can be seen as an extension to reduced Hessian methods of the well known results of Powell (1976) for unconstrained optimization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588794
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  • 2
    Digitale Medien
    Digitale Medien
    A trust region method based on interior point techniques for nonlinear programming (2000)
    Springer
    Mathematical programming 89 (2000), S. 149-185 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Key words: constrained optimization – interior point method – large-scale optimization – nonlinear programming – primal method – primal-dual method – SQP iteration – barrier method – trust region method Mathematics Subject Classification (1991): 20E28, 20G40, 20C20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract. An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described. It applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives. This framework permits primal and primal-dual steps, but the paper focuses on the primal version of the new algorithm. An analysis of the convergence properties of this method is presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/PL00011391
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  • 3
    Digitale Medien
    Digitale Medien
    Numerical Experience with a Reduced Hessian Method for Large Scale Constrained Optimization (2000)
    Springer
    Computational optimization and applications 15 (2000), S. 45-67 
    Details
    ISSN: 1573-2894
    Schlagwort(e): Successive Quadratic Programming ; reduced Hessian methods ; constrained optimization ; quasi-Newton method ; large-scale optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: Abstract The reduced Hessian SQP algorithm presented in Biegler et al. [SIAM J. Optimization, Vol. 5, no. 2, pp. 314–347, 1995.] is developed in this paper into a practical method for large-scale optimization. The novelty of the algorithm lies in the incorporation of a correction vector that approximates the cross term ZTWYpY. This improves the stability and robustness of the algorithm without increasing its computational cost. The paper studies how to implement the algorithm efficiently, and presents a set of tests illustrating its numerical performance. An analytic example, showing the benefits of the correction term, is also presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008723031056
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