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  • 1
    Electronic Resource
    Electronic Resource
    Long-Step Primal Path-Following Algorithm for Monotone Variational Inequality Problems (1998)
    Springer
    Journal of optimization theory and applications 99 (1998), S. 509-531 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; variational inequalities ; Newton method ; interior-point methods ; path-following methods ; barrier-function methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we present a long-step primal path-following algorithm and prove its global convergence under usual assumptions. It is seen that the short-step algorithm is a special case of the long-step algorithm for a specific selection of the parameters and the initial solution. Our theoretical result indicates that the long-step algorithm is more flexible. Numerical results indicate that the long-step algorithm converges faster than the short-step algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021786630040
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  • 2
    Electronic Resource
    Electronic Resource
    On the convergence of projection methods: Application to the decomposition of affine variational inequalities (1995)
    Springer
    Journal of optimization theory and applications 85 (1995), S. 347-362 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; variational inequalities ; projection methods ; decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we first discuss the global convergence of symmetric projection methods for solving nonlinear monotone variational inequalities under a cocoercivity assumption. A similar analysis is applied to asymmetric projection methods, when the mapping is affine and monotone. Under a suitable choice of the projection matrix, decomposition can be achieved. It is proved that this scheme achieves a linear convergence rate, thus enhancing results previously obtained by Tseng (Ref. 1) and by Luo and Tseng (Ref. 2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192231
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  • 3
    Electronic Resource
    Electronic Resource
    Modified Primal Path-Following Scheme for the Monotone Variational Inequality Problem (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 189-208 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; variational inequalities ; interior-point method ; path-following method ; barrier function method ; network equilibrium problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, several interior-point methods have been developed under a scaled Lipschitz condition which may be strong in general. In this paper, we develop a modified path-following scheme which does not require the above condition. Its global convergence is proved under only the assumptions of monotonicity and differentiability of the mapping. The scheme is adapted to the network equilibrium problem (a nonlinear multicommodity network flow problem) with a simplicial decomposition technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022643630525
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