Interior methods for mathematical programs with complementarity constraints

SIAM Journal on Optimization

Volumn 17, Issue 1, 2007, Pages 52-77

  Leyffer, Sven ^a   López Calva, Gabriel ^b   Nocedal, Jorge ^b  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b Northwestern University   (United States)

Author keywords

Complementarity constraints; Equilibrium constraints; Exact penalty; Interior point methods; Mathematical programs with complementarity constraints; Nonlinear programming

Indexed keywords

COMPLEMENTARITY CONSTRAINTS; EQUILIBRIUM CONSTRAINTS; INTERIOR-POINT METHODS; MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS;

ALGORITHMS; CONSTRAINT THEORY; GLOBAL OPTIMIZATION; PROBLEM SOLVING; RELAXATION PROCESSES; ROBUSTNESS (CONTROL SYSTEMS);

MATHEMATICAL PROGRAMMING;

EID: 33847118551     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/040621065     Document Type: Article

References (26)

1. M. ANITESCU, On Solving Mathematical Programs with Complementarity Constraints as Non-linear Programs, Preprint ANL/MCS-P864-1200, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 2000.
2. M. ANITESCU, Global convergence of an elastic mode approach for a class of mathematical programs with complementarity constraints, SIAM J. Optim., 16 (2005), pp. 120-145.
3. H. Y. BENSON, A. SEN, D. F. SHANNO, AND R. J. VANDERBEI, Interior-Point Algorithms, Penalty Methods and Equilibrium Problems, Report ORFE-03-02, Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, 2003.
4. R. H. BYRD, M. E. HRIBAR, AND J. NOCEDAL, An interior point algorithm for large-scale nonlinear programming, SIAM J. Optim., 9 (1999), pp. 877-900.
5. R. H. BYRD, G. LIU, AND J. NOCEDAL, On the local behavior of an interior point method for nonlinear programming, in Numerical Analysis 1997, D. F. Griffiths, D. J. Higham, and G. A. Watson, eds., Addison-Wesley Longman, Harlow, UK, 1997, pp. 37-56.
6. 2-penalty methods for nonlinear programming with strong global convergence properties, Math. Program., to appear.
7. A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, Trust Region Methods, MPS/SIAM Ser. Optim. 1, SIAM, Philadelphia, 2000.
8. V. DEMIGUEL, M. P. FRIEDLANDER, F. J. NOGALES, AND S. SCHOLTES, A two-sided relaxation scheme for mathematical programs with equilibrium constraints, SIAM J. Optim., 16 (2005), pp. 587-609.
9. E. D. DOLAN AND J. J. MORÉ, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), pp. 201-213.
10. M. C. FERRIS AND F. TIN-LOI, On the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints, Comput. Methods Appl. Mech. Engrg., 174 (1999), pp. 107-120.
11. R. FLETCHER AND S. LEYFFER, Nonlinear programming without a penalty function, Math. Program., 91 (2002), pp. 239-269.
12. R. FLETCHER AND S. LEYFFER, Solving mathematical programs with complementarity constraints as nonlinear programs, Optim. Methods Softw., 19 (2004), pp. 15-40.
13. R. FLETCHER, S. LEYFFER, D. RALPH, AND S. SCHOLTES, Local convergence of SQP methods for mathematical programs with equilibrium constraints, SIAM J. Optim., to appear.
14. A. FORSGREN, P. E. GILL, AND M. H. WRIGHT, Interior methods for nonlinear optimization, SIAM Rev., 44 (2002), pp. 525-597.
15. P. E. GILL, W. MURRAY, AND M. A. SAUNDERS, SNOPT: An SQP algorithm for large-scale constrained optimization, SIAM J. Optim., 12 (2002), pp. 979-1006.
16. N. I. M. GOULD, D. ORBAN, AND PH. TOINT, An Interior-Point l1-Penalty Method for Non-linear Optimization, Tech. report RAL-TR-2003-022, Rutherford Appleton Laboratory Chilton, Oxfordshire, UK, 2003.
17. X. M. HU AND D. RALPH, Convergence of a penalty method for mathematical programming with complementarity constraints, J. Optim. Theory Appl., 123 (2004), pp. 365-390.
18. S. LEYFFER, MacMPEC: AMPL Collection of MPECs, http://www.mcs.anl.gov/~leyffer/MacMPEC (5 August 2005).
19. X. LIU AND J. SUN, Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints, Math. Program., 101 (2004), pp. 231-261.
20. G. LÓPEZ-CALVA, Exact-Penalty Methods for Nonlinear Programming, Ph.D. thesis, Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, 2005.
21. A. U. RAGHUNATHAN AND L. T. BIEGLER, An interior point method for mathematical programs with complementarity constraints (MPCCs), SIAM J. Optim., 15 (2005), pp. 720-750.
22. D. RALPH AND S. J. WRIGHT, Some properties of regularization and penalization schemes for MPECs, Optim. Methods. Softw., 19 (2004), pp. 527-556.
23. H. SCHEEL AND S. SCHOLTES, Mathematical programs with complementarity constraints: Stationarity, optimality and sensitivity, Math. Oper. Res., 25 (2000), pp. 1-22.
24. S. SCHOLTES, Convergence properties of a regularization scheme for mathematical programs with complementarity constraints, SIAM J. Optim., 11 (2001), pp. 918-936.
25. R. J. VANDERBEI AND D. F. SHANNO, An interior point algorithm for nonconvex nonlinear programming, Comput. Optim. Appl., 13 (1999), pp. 231-252.
26. R. A. WALTZ, J. L. MORALES, J. NOCEDAL, AND D. ORBAN, An interior algorithm for nonlinear optimization that combines line search and trust region steps, Math. Program., to appear.