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  • 1
    Electronic Resource
    Electronic Resource
    Local convergence of predictor—corrector infeasible-interior-point algorithms for SDPs and SDLCPs (1998)
    Springer
    Mathematical programming 80 (1998), S. 129-160 
    Details
    ISSN: 1436-4646
    Keywords: Semidefinite programming ; Infeasible-interior-point method ; Predictor—correctormethod ; Superlinear convergence ; Primal—dual nondegeneracy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An example of an SDP (semidefinite program) exhibits a substantial difficulty in proving the superlinear convergence of a direct extension of the Mizuno—Todd—Ye type predictor—corrector primal-dual interior-point method for LPs (linear programs) to SDPs, and suggests that we need to force the generated sequence to converge to a solution tangentially to the central path (or trajectory). A Mizuno—Todd—Ye type predictor—corrector infeasible-interior-point algorithm incorporating this additional restriction for monotone SDLCPs (semidefinite linear complementarity problems) enjoys superlinear convergence under strict complementarity and nondegeneracy conditions. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581723
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  • 2
    Electronic Resource
    Electronic Resource
    Change of generalized indices of stationary solutions. to multiparametric optimization (2000)
    Springer
    Mathematical programming 88 (2000), S. 193-210 
    Details
    ISSN: 1436-4646
    Keywords: Key words: multiparametric optimization – generalized index – regular value condition – existence of locally bounded Lagrange multiplier vector
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We study the local change of the generalized index, which is a modification of the Morse index and the stationary index, for the multiparametric optimization. Under the Regular Value Condition, the change of the generalized index around a triplet (x,v,t) is locally bounded by the dimension of the parameter vector t, where x is a variable vector and v a vector of the Lagrange multiplier space. We also discuss the local change of the generalized index around a pair (x,t).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00011374
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  • 3
    Electronic Resource
    Electronic Resource
    Search directions in the SDP and the monotone SDLCP: generalization and inexact computation (1999)
    Springer
    Mathematical programming 85 (1999), S. 51-80 
    Details
    ISSN: 1436-4646
    Keywords: Key words: interior-point methods – semidefinite programming – semidefinite linear complementarity problem – inexact computation – search direction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s101070050046
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