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Improved convergence properties of the LinFukushimaRegularization method for mathematical programs with complementarity constraints
1.  University of Würzburg, Institute of Mathematics, Am Hubland, 97074 Würzburg, Germany, Germany, Germany 
References:
[1] 
M. S. Bazaraa and C. M. Shetty, "Foundations of Optimization,'' Lecture Notes in Economics and Mathematical Systems, SpringerVerlag, Berlin/Heidelberg, 1976. Google Scholar 
[2] 
Y. Chen and M. Florian, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions, Optimization, 32 (1995), 193209. doi: 10.1080/02331939508844048. Google Scholar 
[3] 
A. V. Demiguel, M. P. Friedlander, F. J. Nogales and S. Scholtes, A twosided relaxation scheme for mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 16 (2005), 587609. doi: 10.1137/04060754x. Google Scholar 
[4] 
S. Dempe, "Foundations of Bilevel Programming, Nonconvex Optimization and Its Applications," 61 (2002), Kluwer Academic Publishers, Dordrecht, The Netherlands . Google Scholar 
[5] 
M. L. Flegel and C. Kanzow, On the Guignard constraint qualification for mathematical programs with equilibrium constraints, Optimization, 54 (2005), 517534. doi: 10.1080/02331930500342591. Google Scholar 
[6] 
M. L. Flegel and C. Kanzow, A direct proof for Mstationarity under MPECACQ for mathematical programs with equilibrium constraints, In "Optimization with Multivalued Mappings: Theory, Applications and Algorithms''(eds. S. Dempe and V. Kalashnikov), SpringerVerlag, New York, 2006, 111122. doi: 10.1007/0387342214_6. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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), 78103. doi: 10.1137/070705490. Google Scholar 
[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. Google Scholar 
[11] 
S. Leyffer, MacMPEC: AMPL collection of MPECs, www.mcs.anl.go/~leyffer/MacMPEC, 2000. Google Scholar 
[12] 
G. H. Lin and M. Fukushima, A modified relaxation scheme for mathematical programs with complementarity constraints, Annals of Operations Research, 133 (2005), 6384. doi: 10.1007/s104790045024z. Google Scholar 
[13] 
, www.netlib.org/ampl/solvers, /examples/amplfunc.c, (). Google Scholar 
[14] 
Z. Q. Luo, J. S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints,'' Cambridge University Press, Cambridge, New York, Melbourne, 1996. Google Scholar 
[15] 
O. L. Mangasarian, "Nonlinear Programming,'' McGrawHill, New York, NY, 1969 (reprinted by SIAM, Philadelphia, PA, 1994). Google Scholar 
[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. Google Scholar 
[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), 963981. doi: 10.1137/S1052623497326629. Google Scholar 
[18] 
H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity, Mathematics of Operations Research, 25 (2000), 122. doi: 10.1287/moor.25.1.1.15213. Google Scholar 
[19] 
S. Scholtes, Convergence properties of a regularization scheme for mathematical programs with complementarity constraints, SIAM Journal on Optimization, 11 (2001), 918936. doi: 10.1137/S1052623499361233. Google Scholar 
[20] 
S. Steffensen and M. Ulbrich, A new relaxation scheme for mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 20 (2010), 25042539. doi: 10.1137/090748883. Google Scholar 
[21] 
J. J. Ye, Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints, SIAM Journal on Optimization, 10 (2000), 943962. doi: 10.1137/S105262349834847X. Google Scholar 
[22] 
J. J. Ye and D. L. Zhu, Optimality conditions for bilevel programming problems, Optimization, 33 (1995), 927. doi: 10.1080/02331939508844060. Google Scholar 
show all references
References:
[1] 
M. S. Bazaraa and C. M. Shetty, "Foundations of Optimization,'' Lecture Notes in Economics and Mathematical Systems, SpringerVerlag, Berlin/Heidelberg, 1976. Google Scholar 
[2] 
Y. Chen and M. Florian, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions, Optimization, 32 (1995), 193209. doi: 10.1080/02331939508844048. Google Scholar 
[3] 
A. V. Demiguel, M. P. Friedlander, F. J. Nogales and S. Scholtes, A twosided relaxation scheme for mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 16 (2005), 587609. doi: 10.1137/04060754x. Google Scholar 
[4] 
S. Dempe, "Foundations of Bilevel Programming, Nonconvex Optimization and Its Applications," 61 (2002), Kluwer Academic Publishers, Dordrecht, The Netherlands . Google Scholar 
[5] 
M. L. Flegel and C. Kanzow, On the Guignard constraint qualification for mathematical programs with equilibrium constraints, Optimization, 54 (2005), 517534. doi: 10.1080/02331930500342591. Google Scholar 
[6] 
M. L. Flegel and C. Kanzow, A direct proof for Mstationarity under MPECACQ for mathematical programs with equilibrium constraints, In "Optimization with Multivalued Mappings: Theory, Applications and Algorithms''(eds. S. Dempe and V. Kalashnikov), SpringerVerlag, New York, 2006, 111122. doi: 10.1007/0387342214_6. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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), 78103. doi: 10.1137/070705490. Google Scholar 
[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. Google Scholar 
[11] 
S. Leyffer, MacMPEC: AMPL collection of MPECs, www.mcs.anl.go/~leyffer/MacMPEC, 2000. Google Scholar 
[12] 
G. H. Lin and M. Fukushima, A modified relaxation scheme for mathematical programs with complementarity constraints, Annals of Operations Research, 133 (2005), 6384. doi: 10.1007/s104790045024z. Google Scholar 
[13] 
, www.netlib.org/ampl/solvers, /examples/amplfunc.c, (). Google Scholar 
[14] 
Z. Q. Luo, J. S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints,'' Cambridge University Press, Cambridge, New York, Melbourne, 1996. Google Scholar 
[15] 
O. L. Mangasarian, "Nonlinear Programming,'' McGrawHill, New York, NY, 1969 (reprinted by SIAM, Philadelphia, PA, 1994). Google Scholar 
[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. Google Scholar 
[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), 963981. doi: 10.1137/S1052623497326629. Google Scholar 
[18] 
H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity, Mathematics of Operations Research, 25 (2000), 122. doi: 10.1287/moor.25.1.1.15213. Google Scholar 
[19] 
S. Scholtes, Convergence properties of a regularization scheme for mathematical programs with complementarity constraints, SIAM Journal on Optimization, 11 (2001), 918936. doi: 10.1137/S1052623499361233. Google Scholar 
[20] 
S. Steffensen and M. Ulbrich, A new relaxation scheme for mathematical programs with equilibrium constraints, SIAM Journal on Optimization, 20 (2010), 25042539. doi: 10.1137/090748883. Google Scholar 
[21] 
J. J. Ye, Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints, SIAM Journal on Optimization, 10 (2000), 943962. doi: 10.1137/S105262349834847X. Google Scholar 
[22] 
J. J. Ye and D. L. Zhu, Optimality conditions for bilevel programming problems, Optimization, 33 (1995), 927. doi: 10.1080/02331939508844060. Google Scholar 
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