Elastic-mode algorithms for mathematical programs with equilibrium constraints: Global convergence and stationarity properties

Mathematical Programming

Volumn 110, Issue 2, 2007, Pages 337-371

  Anitescu, Mihai ^a   Tseng, Paul ^b   Wright, Stephen J ^c  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

^c University of Wisconsin   (United States)

Author keywords

C stationarity; Complementarity constraints; Elastic mode formulation; Equilibrium constraints; M stationarity; Nonlinear programming; Strong stationarity

Indexed keywords

CONSTRAINED OPTIMIZATION; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; PROBLEM SOLVING; THEOREM PROVING;

C-STATIONARITY; COMPLEMENTARITY CONSTRAINTS; ELASTIC MODE FORMULATION; EQUILIBRIUM CONSTRAINTS; M-STATIONARITY; STRONG STATIONARITY;

NONLINEAR PROGRAMMING;

EID: 33947682809     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0005-4     Document Type: Article

References (24)

1. Anitescu, M.: On using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints. SIAM J. Optim. 15, 1203-1236 (2005)
2. Anitescu, M.: Global convergence of an elastic mode approach for a class of mathematical programs with complementarity constraints. SIAM J. Optim. 16, 120-145 (2005)
3. DeMiguel, A., Friedlander, M., Nogales, F.J., Scholtes, &: An interior-point method for MPECs based on strictly feasible relaxations, Preprint ANL/MCS-P1150-0404, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, USA, Argonne, IL, USA (2004)
4. Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. Ser. A 91, 239-269 (2002)
5. Fletcher, R., Leyffer, S.: Numerical experience with solving MPECs as NLPs, Report NA/210, University of Dundee (2002)
6. Fukushima, M., Pang, J.-S.: Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. In: Théra, M., Tichatschke, R. (eds.) Ill-posed Variational Problems and Regularization Techniques, vol. 477 of Lecture Notes in Economics and Mathematical Systems, Springer, Berlin Heidelberg New York, pp. 99-110 (1999)
7. 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, 724-739 (2002)
8. Gay, D.M.: Hooking your solver to AMPL, technical report, Bell Laboratories. Murray Hill, NJ, 1993. Revised 1994, 1997
9. Hu, X.M., Ralph, D.: Convergence of a penalty method for mathematical programming with complementarity constraints. J. Optim. Theory Appl. 123, 365-390 (2004)
10. Jongen, H.T., Jonker, P., Twilt, F.: Critical sets in parametric optimization. Math. Program. 34, 333-353 (1986)
11. Jongen, H.T., Jonker, P., Twill, E: One-parameter families of optimization problems: Equality constraints. J Optim. Theory Appl. 48, 141-161 (1986)
12. Kocvara, M., Outrata, J.: Optimization problems with equilibrium constraints and their numerical solution. Math. Program. 101, 119-149 (2004)
13. Leyffer, S.: MacMPEC AMPL collection of mathematical programs with equilibrium constraints
14. Lin, G.H., Fukushima, M.: New relaxation method for mathematical programs with complementarity constraints. J. Optim. Theory Appl. 118, 81-116 (2003)
15. Liu, X., Sun, J.: Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints. Math. Program. 101, 231-261 (2004)
16. Luo, Z.-Q., Pang, J.-S., Ralph, D.: Piecewise sequential quadratic programming for mathematical programs with nonlinear complementarity constraints. In: Migdalas, A., Pardalos, P., Varbrand, P. (eds.) Multilevel Optimization: Algorithms, Complexity and Applications. Kluwer, Dordrecht, pp. 209-229 (1998)
17. Outrata, J.: Optimality conditions for a class of mathematical programs with equilibrium constraints. Math. Oper. Res. 24, 627-644 (1999)
18. Outrata, J., Kocvara, M., Zowe, J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications, and Numerical Results. Kluwer, Dordrecht (1998)
19. Overton, M.L.: Numerical Computing with IEEE Floating-Point Arithmetic. SIAM (2001)
20. Ralph, D., Wright, S.J.: Some properties of regularization and penalization schemes for MPECs. Optim. Methods Softw. 19, 527-556 (2004)
21. Robinson, S.M.: Generalized equations and their solutions. Part II: Applications to nonlinear programming. Math. Program. Study 19, 200-221 (1982)
22. Scheel, H., Scholtes, S.: Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Math. Oper. Res. 25, 1-22 (2000)
23. Scholtes, S.: Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 11, 918-936 (2001)
24. Scholtes, S., Stöhr, M.: How stringent is the linear independence assumption for mathematical programs with complementarity constraints? Math. Oper. Res. 26, 851-863 (2001)