[1] Anitescu, M.: Global convergence of an elastic mode approach for a class of mathematical programs with complementarity constraints. SIAM J. Optim. 16 (2005), 120-145. DOI 10.1137/040606855 | MR 2177772 | Zbl 1099.65050

[2] Anitescu, M.: On using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints. SIAM J. Optim. 15 (2005), 1203-1236. DOI 10.1137/s1052623402401221 | MR 2178496 | Zbl 1097.90050

[3] Biegler, L. T., Raghunathan, A. U.: An interior point method for mathematical programs with complementarity constraints (MPCCs). SIAM J. Optim. 15 (2005), 720-750. DOI 10.1137/s1052623403429081 | MR 2142858 | Zbl 1077.90079

[4] DeMiguel, V., Friedlander, M. P., Nogales, F. J., Scholtes, S.: A two-sided relaxation scheme for mathematical programs with equilibrium constraints. SIAM J. Optim. 16 (2005), 587-609. DOI 10.1137/04060754x | MR 2197997 | Zbl 1122.90060

[5] Facchinei, F., Jiang, H., Qi, L.: A smoothing method for mathematical programs with equilibrium constraints. Math. Programming 85 (1999), 107-134. DOI 10.1007/s101070050048 | MR 1689366 | Zbl 0959.65079

[6] Fletcher, R.: Practical Methods of Optimization 2: Constrained Optimization. John Wiley and Sons, Chichester 1981. MR 0633058

[7] Fletcher, R., Leyffer, S.: Solving mathematical programs with complementary constraints as nonlinear programs. Zbl 1074.90044

[8] Fletcher, R., Leyffer, S., Ralph, D., Scholtes, S.: Local convergence of SQP methods for mathematical programs with equilibrium constraints. SIAM J. Optim. 17 (2006), 259-286. DOI 10.1137/s1052623402407382 | MR 2219153 | Zbl 1112.90098

[9] Fukushima, M., Tseng, P.: An implementable active-set algorithm for computing a b-stationary point of a mathematical program with linear complementarity constraints. SIAM J. Optim. 12 (2002), 724-739. DOI 10.1137/s1052623499363232 | MR 1884914 | Zbl 1127.65034

[10] Gfrerer, H.: Optimality conditions for disjunctive programs based on generalized differentiation with application to mathematical programs with equilibrium constraints. SIAM J. Optim. 24 (2014), 898-931. DOI 10.1137/130914449 | MR 3217222 | Zbl 1298.49021

[11] Giallombardo, G., Ralph, D.: Multiplier convergence in trust region methods with application to convergence of decomposition methods for MPECs. Math. Programming 112 (2008), 335-369. DOI 10.1007/s10107-006-0020-5 | MR 2361928 | Zbl 1145.90073

[12] Hu, X. M., Ralph, D.: Convergence of a penalty method for mathematical programming with complementarity constraints. J. Optim. Theory Appl. 123 (2004), 365-390. DOI 10.1007/s10957-004-5154-0 | MR 2101411

[13] Izmailov, A. F., Pogosyan, A. L., Solodov, M. V.: Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints. Computational Optim. Appl. 51 (2012), 199-221. DOI 10.1007/s10589-010-9341-7 | MR 2872496 | Zbl 1245.90124

[14] Jiang, H., Ralph, D.: QPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints. Comput. Optim. Appl. 13 (1999), 25-59. DOI 10.1023/A:1008696504163 | MR 1704113

[15] Jiang, H., Ralph, D.: Extension of quasi-newton methods to mathematical programs with complementarity constraints. Comput. Optim. Appl. 25 (2002), 123-150. DOI 10.1023/A:1022945316191 | MR 1996665 | Zbl 1038.90100

[16] Kadrani, A., Dussault, J. P., Benchakroun, A.: A new regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 20 (2009), 78-103. DOI 10.1137/070705490 | MR 2496894 | Zbl 1187.65064

[17] Kanzow, C., Schwartz, A.: A new regularization method for mathematical programs with complementarity constraints with strong convergence properties. SIAM J. Optim. 23 (2013), 770-798. DOI 10.1137/100802487 | MR 3045664 | Zbl 1282.65069

[18] Kanzow, C., Schwartz, A.: The price of inexactness: convergence properties of relaxation methods for mathematical programs with equilibrium constraints revisited. Math. Oper. Res. 40 (2015), 2, 253-275. DOI 10.1287/moor.2014.0667 | MR 3320430

[19] Leyffer, S.: MacMPEC: AMPL collection of MPECs, 2000. DOI 

[20] Leyffer, S., López-Calva, G., Nocedal, J.: Interior methods for mathematical programs with complementarity constraints. SIAM J. Optim. 17 (2006), 52-77. DOI 10.1137/040621065 | MR 2219144 | Zbl 1112.90095

[21] Lin, G. H., Fukushima, M.: A modified relaxation scheme for mathematical programs with complementarity constraints. Ann. Oper. Res. 133 (2005), 63-84. DOI 10.1007/s10479-004-5024-z | MR 2119313 | Zbl 1119.90058

[22] Luo, Z. Q., Pang, J. S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, New York, Melbourne 1996. DOI 10.1017/cbo9780511983658 | MR 1419501 | Zbl 1139.90003

[23] Luo, Z. Q., Pang, J. S., Ralph, D.: Piecewise sequential quadratic programming for mathematical programs with nonlinear complementarity constraints. In: Multilevel Optimization: Algorithms, Complexity, and Applications (A. Migdalas, P. Pardalos, and P. Värbrand, eds.), Kluwer Academic Publishers, Dordrecht 1998, pp. 209-229. DOI 10.1007/978-1-4613-0307-7_9 | MR 1605239 | Zbl 0897.90184

[24] Luo, Z. Q., Pang, J. S., Ralph, D., Wu, S. Q.: Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints. Math. Programming 75 (1996), 19-76. DOI 10.1007/bf02592205 | MR 1415093 | Zbl 0870.90092

[25] Outrata, J. V., Kočvara, M., Zowe, J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints, Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht 1998. DOI 10.1007/978-1-4757-2825-5 | MR 1641213

[26] Powell, M. J. D.: A fast algorithm for nonlinearly constrained optimization calculations. In: Numerical Analysis Dundee 1977 (G. A. Watson, ed.), Lecture Notes in Mathematics 630, Springer, Berlin, 1978, pp. 144-157. DOI 10.1007/bfb0067703 | MR 0483447 | Zbl 0374.65032

[27] Ralph, D., Wright, S. J.: Some properties of regularization and penalization schemes for MPECs. Optim. Methods Software 19 (2004), 527-556. DOI 10.1080/10556780410001709439 | MR 2095351 | Zbl 1097.90054

[28] Scheel, H., Scholtes, S.: Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Math. Oper. Res. 25 (2000), 1-22. DOI 10.1287/moor.25.1.1.15213 | MR 1854317 | Zbl 1073.90557

[29] Scholtes, S.: Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 11 (2001), 918-936. DOI 10.1137/s1052623499361233 | MR 1855214 | Zbl 1010.90086

[30] Scholtes, S., Stöhr, M.: Exact penalization of mathematical programs with equilibrium constraints. SIAM J. Control Optim. 37 (1999), 617-652. DOI 10.1137/s0363012996306121 | MR 1670641 | Zbl 0922.90128

[31] Steffensen, S., Ulbrich, M.: A new regularization scheme for mathematical programs with equilibrium constraints. SIAM J. Optim. 20 (2010), 2504-2539. DOI 10.1137/090748883 | MR 2678403

[32] Stein, O.: Lifting mathematical programs with complementarity constraints. Math. Programming 131 (2012), 71-94. DOI 10.1007/s10107-010-0345-y | MR 2886141 | Zbl 1250.90094

[33] Stöhr, M.: Nonsmooth Trust Region Methods and their Applications to Mathematical Programs with Equilibrium Constraints. Shaker-Verlag, Aachen 1999.

[34] Zhang, J., Liu, G.: A new extreme point algorithm and its application in psqp algorithms for solving mathematical programs with linear complementarity constraints. J. Glob. Optim. 19 (2001), 335-361. DOI 10.1023/A:1011226232107 | MR 1824769 | Zbl 1049.90125