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Improved convergence properties of the Lin-Fukushima-Regularization method for mathematical programs with complementarity constraints

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  • We consider a regularization method for the numerical solution of mathematical programs with complementarity constraints (MPCC) introduced by Gui-Hua Lin and Masao Fukushima. Existing convergence results are improved in the sense that the MPCC-LICQ assumption is replaced by the weaker MPCC-MFCQ. Moreover, some preliminary numerical results are presented in order to illustrate the theoretical improvements.
    Mathematics Subject Classification: 65K05, 90C30, 90C31.

    Citation:

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  • [1]

    M. S. Bazaraa and C. M. Shetty, "Foundations of Optimization,'' Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin/Heidelberg, 1976.

    [2]

    Y. Chen and M. Florian, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions, Optimization, 32 (1995), 193-209.doi: 10.1080/02331939508844048.

    [3]

    A. V. Demiguel, M. P. Friedlander, F. J. Nogales and S. Scholtes, A two-sided relaxation scheme for mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 16 (2005), 587-609.doi: 10.1137/04060754x.

    [4]

    S. Dempe, "Foundations of Bilevel Programming, Nonconvex Optimization and Its Applications," 61 (2002), Kluwer Academic Publishers, Dordrecht, The Netherlands .

    [5]

    M. L. Flegel and C. Kanzow, On the Guignard constraint qualification for mathematical programs with equilibrium constraints, Optimization, 54 (2005), 517-534.doi: 10.1080/02331930500342591.

    [6]

    M. L. Flegel and C. Kanzow, A direct proof for M-stationarity under MPEC-ACQ for mathematical programs with equilibrium constraints, In "Optimization with Multivalued Mappings: Theory, Applications and Algorithms''(eds. S. Dempe and V. Kalashnikov), Springer-Verlag, New York, 2006, 111-122.doi: 10.1007/0-387-34221-4_6.

    [7]

    T. Hoheisel, C. Kanzow and A. Schwartz, Convergence of a local regularization approach for mathematical programs with complementarity or vanishing constraints, Preprint 293, Institute of Mathematics, University of Würzburg, Würzburg, February 2010.

    [8]

    T. Hoheisel, C. Kanzow and A. Schwartz, Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints, Preprint 299, Institute of Mathematics, University of Würzburg, Würzburg, September 2010.

    [9]

    A. Kadrani, J. P. Dussault and A. Benchakroun, A new regularization scheme for mathematical programs with complementarity constraints, SIAM Journal on Optimization, 20 (2009), 78-103.doi: 10.1137/070705490.

    [10]

    C. Kanzow and A. Schwartz, A new regularization method for mathematical programs with complementarity constraints with strong convergence properties, Preprint 296, Institute of Mathematics, University of Würzburg, Würzburg, June 2010.

    [11]

    S. Leyffer, MacMPEC: AMPL collection of MPECs, www.mcs.anl.go/~leyffer/MacMPEC, 2000.

    [12]

    G. H. Lin and M. Fukushima, A modified relaxation scheme for mathematical programs with complementarity constraints, Annals of Operations Research, 133 (2005), 63-84.doi: 10.1007/s10479-004-5024-z.

    [13]
    [14]

    Z. Q. Luo, J. S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints,'' Cambridge University Press, Cambridge, New York, Melbourne, 1996.

    [15]

    O. L. Mangasarian, "Nonlinear Programming,'' McGraw-Hill, New York, NY, 1969 (reprinted by SIAM, Philadelphia, PA, 1994).

    [16]

    J. V. Outrata, M. Kočvara and J. Zowe, "Nonsmooth Approach to Optimization Problems with Equilibrium Constraints,'' Nonconvex Optimization and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.

    [17]

    L. Qi and Z. Wei, On the constant positive linear dependence condition and its applications to SQP methods, SIAM Journal on Optimization, 10 (2000), 963-981.doi: 10.1137/S1052623497326629.

    [18]

    H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity, Mathematics of Operations Research, 25 (2000), 1-22.doi: 10.1287/moor.25.1.1.15213.

    [19]

    S. Scholtes, Convergence properties of a regularization scheme for mathematical programs with complementarity constraints, SIAM Journal on Optimization, 11 (2001), 918-936.doi: 10.1137/S1052623499361233.

    [20]

    S. Steffensen and M. Ulbrich, A new relaxation scheme for mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 20 (2010), 2504-2539.doi: 10.1137/090748883.

    [21]

    J. J. Ye, Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints, SIAM Journal on Optimization, 10 (2000), 943-962.doi: 10.1137/S105262349834847X.

    [22]

    J. J. Ye and D. L. Zhu, Optimality conditions for bilevel programming problems, Optimization, 33 (1995), 9-27.doi: 10.1080/02331939508844060.

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