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  • asymptotic expansions  (1)
  • projective algorithms  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Monotone Variable–Metric Algorithm for Linearly Constrained Nonlinear Programming (2000)
    Springer
    Journal of optimization theory and applications 104 (2000), S. 255-279 
    Details
    ISSN: 1573-2878
    Keywords: nonlinear programming ; path-following methods ; differential equations ; projective algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new method for linearly constrained nonlinear programming is proposed. This method follows affine scaling paths defined by systems of ordinary differential equations and it is fully parallelizable. The convergence of the method is proved for a nondegenerate problem with pseudoconvex objective function. In practice, the algorithm works also under more general assumptions on the objective function. Numerical results obtained with this computational method on several test problems are shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004645328197
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  • 2
    Electronic Resource
    Electronic Resource
    Inverse Problem for a Class of Two-Dimensional Diffusion Equations with Piecewise Constant Coefficients (1999)
    Springer
    Journal of optimization theory and applications 100 (1999), S. 29-57 
    Details
    ISSN: 1573-2878
    Keywords: Inverse problems ; diffusion equations ; spectral measures ; asymptotic expansions ; nonlinear least squares
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider an inverse problem for a class of two-dimensional diffusion equations with piecewise constant coefficients. This problem is studied using an explicit formula for the relevant spectral measures and an asymptotic expansion of the solution of the diffusion equations. A numerical method that reduces the inverse problem to a sequence of nonlinear least-square problems is proposed and tested on synthetic data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021712830465
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