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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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    Paper (German National Licenses)
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  • 2
    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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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Semidefinite Programming Relaxation for Nonconvex Quadratic Programs (1997)
    Springer
    Journal of global optimization 10 (1997), S. 367-380 
    Details
    ISSN: 1573-2916
    Keywords: Semidefinite program ; relaxation method ; interior-point method ; nonconvex quadratic program ; linear matrix inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper applies the SDP (semidefinite programming)relaxation originally developed for a 0-1 integer program to ageneral nonconvex QP (quadratic program) having a linear objective functionand quadratic inequality constraints, and presents some fundamental characterizations of the SDP relaxation including its equivalence to arelaxation using convex-quadratic valid inequalities for the feasible regionof the QP.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008282830093
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Basic lemmas in polynomial-time infeasible-interiorpoint methods for linear programs (1996)
    Springer
    Annals of operations research 62 (1996), S. 1-28 
    Details
    ISSN: 1572-9338
    Keywords: Linear program ; interior point method ; initial point ; step length ; complementarity problem ; polynomial-time complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The primal-dual infeasible-interior-point algorithm is known as one of the most efficient computational methods for linear programs. Recently, a polynomial-time computational complexity bound was established for special variants of the algorithm. However, they impose severe restrictions on initial points and require a common step length in the primal and dual spaces. This paper presents some basic lemmas that bring great flexibility and improvement into such restrictions on initial points and step lengths, and discusses their extensions to linear and nonlinear monotone complementarity problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02206809
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    Paper (German National Licenses)
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