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  • 1
    Electronic Resource
    Electronic Resource
    Partitioned quasi-Newton methods for nonlinear equality constrained optimization (1992)
    Springer
    Mathematical programming 53 (1992), S. 17-44 
    Details
    ISSN: 1436-4646
    Keywords: 65H10 ; 65K05 ; 65K10 ; Constrained optimization ; equality constraints ; numerical optimization ; quasi-Newton method ; secant method ; sequential quadratic programming ; SQP-method ; augmented Lagrangian method ; penalty function methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We derive new quasi-Newton updates for the (nonlinear) equality constrained minimization problem. The new updates satisfy a quasi-Newton equation, maintain positive definiteness on the null space of the active constraint matrix, and satisfy a minimum change condition. The application of the updates is not restricted to a small neighbourhood of the solution. In addition to derivation and motivational remarks, we discuss various numerical subtleties and provide results of numerical experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585692
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A globally and quadratically convergent affine scaling method for linearℓ 1 problems (1992)
    Springer
    Mathematical programming 56 (1992), S. 189-222 
    Details
    ISSN: 1436-4646
    Keywords: 65H10 ; 65K05 ; 65K10 ; Linearℓ 1 estimation ; linear programming ; interior-point algorithm ; simplex method ; least absolute value regression ; affine scaling method ; Karmarkar
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently, various interior point algorithms related to the Karmarkar algorithm have been developed for linear programming. In this paper, we first show how this “interior point” philosophy can be adapted to the linear ℓ1 problem (in which there are no feasibility constraints) to yield a globally and linearly convergent algorithm. We then show that the linear algorithm can be modified to provide aglobally and ultimatelyquadratically convergent algorithm. This modified algorithm appears to be significantly more efficient in practise than a more straightforward interior point approach via a linear programming formulation: we present numerical results to support this claim.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580899
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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