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  • 1
    Electronic Resource
    Electronic Resource
    A Quasi-Newton Quadratic Penalty Method for Minimization Subject to Nonlinear Equality Constraints (2000)
    Springer
    Computational optimization and applications 15 (2000), S. 103-123 
    Details
    ISSN: 1573-2894
    Keywords: nonlinearly constrained optimization ; equality constraints ; quasi-Newton methods ; BFGS ; quadratic penalty function ; reduced Hessian approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We present a modified quadratic penalty function method for equality constrained optimization problems. The pivotal feature of our algorithm is that at every iterate we invoke a special change of variables to improve the ability of the algorithm to follow the constraint level sets. This change of variables gives rise to a suitable block diagonal approximation to the Hessian which is then used to construct a quasi-Newton method. We show that the complete algorithm is globally convergent. Preliminary computational results are reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008730909894
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An Exterior Newton Method for Strictly Convex Quadratic Programming (2000)
    Springer
    Computational optimization and applications 15 (2000), S. 5-32 
    Details
    ISSN: 1573-2894
    Keywords: convex quadratic programming ; exterior methods ; Newton methods ; dual problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We propose an exterior Newton method for strictly convex quadratic programming (QP) problems. This method is based on a dual formulation: a sequence of points is generated which monotonically decreases the dual objective function. We show that the generated sequence converges globally and quadratically to the solution (if the QP is feasible and certain nondegeneracy assumptions are satisfied). Measures for detecting infeasibility are provided. The major computation in each iteration is to solve a KKT-like system. Therefore, given an effective symmetric sparse linear solver, the proposed method is suitable for large sparse problems. Preliminary numerical results are reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008773230148
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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