Nonlinear-programming reformulation of the order-value optimization problem

Mathematical Methods of Operations Research

Volumn 61, Issue 3, 2005, Pages 365-384

  Andreani, R ^a   Dunder, C ^b   Martinez J M ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Equilibrium constraints; Nonlinear programming; Optimality conditions; Optimization algorithms; Order value optimization

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; DECISION MAKING; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS);

EQUILIBRIUM CONSTRAINTS; OPTIMIZATION ALGORITHM; OPTIMIZATION CONDITIONS; ORDER-VALUE OPTIMIZATION;

NONLINEAR PROGRAMMING;

EID: 23744464768     PISSN: 14322994     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001860400410     Document Type: Article

References (23)

1. J Abadie, J Carpentier (1968) Generalization of the Wolfe Reduced-Gradient Method to the Case of Nonlinear Constraints. In: Optimization, Edited by R. Fletcher, Academic Press, New York, pp. 37-47
2. R Andreani, C Dunder, JM Martinez (2003) Order-Value Optimization: formulation and solution by means of a primal Cauchy method. Mathematical Methods of Operations Research 58:387-399
3. R Andreani, JM Martinez (2001) On the solution of mathematical programming problems with equilibrium constraints. Mathematical Methods of Operations Research 54:345-358
4. D Bertsekas (1998) Nonlinear Programming, 2nd edition, Athena Scientific, Belmont, Massachusetts
5. RH Byrd, ME Hribar, J Nocedal (1999) An interior point algorithm for large-scale nonlinear programming, SIAM Journal on Optimization 9:877-900
6. JE Dennis, M El-Alem, MC Maciel (1997) A Global Convergence Theory for General Trust-Region-Based Algorithms for Equality Constrained Optimization. SIAM Journal on Optimization 7:177-207
7. MC Ferris, SP Dirkse, A Meeraus (2002) Mathematical programs with equilibrium constraints: Automatic reformulation and solution via constrained optimization. Numerical Analysis Group Research Report NA 02-11, Oxford University Computing Laboratory, Oxford University
8. R Fletcher (1987) Practical Methods Optimization. Wiley, New York
9. R Fletcher, S Leyffer (2002) Numerical experience with solving MPECs as NLPs. University of Dundee Report NA 210
10. R Fletcher, S Leyffer, D Ralph, S Scholtes (2002) Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints. University of Dundee Report NA 209
11. FM Gomes, MC Maciel, JM Martinez (1999) Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters. Mathematical Programming 84:161-200
12. PJ Huber (1981) Robust statistics. Wiley, New York
13. P Jorion (2001) Value at risk: the new benchmark for managing financial risk, 2nd edition. Me Graw-Hill, New York
14. N Krejić, JM Martinez, MP Mello, EA Pilotta (2000) Validation of an Augmented Lagrangian algorithm with a Gauss-Newton Hessian approximation using a set of hard-spheres problems. Computational Optimization and Applications 16:247-263
15. LS Lasdon (1982) Reduced Gradient Methods. In: Nonlinear Optimization 1981, Edited by M. J. D. Powell. Academic Press, New York, 235-242
16. Z-Q Luo, J-S Pang, D Ralph (1996) Mathematical programs with Equilibrium Constraints. Cambridge University Press, Cambridge
17. OL Mangasarian, S Fromovitz (1967) Fritz-John necessary optimality conditions in presence of equality and inequality constraints. Journal of Mathematical Analysis and Applications 17:37-42
18. JM Martinez (2001) Inexact-restoration method with Lagrangian tangent decrease and new merit function for nonlinear programming. Journal of Optimization Theory and Applications 111:39-58
19. JM Martinez, EA Pilotta (2000) Inexact restoration algorithm for constrained optimization, Journal of Optimization Theory and Applications 104:135-163
20. A Miele, HY Huang, JC Heideman (1969) Sequential Gradient-Restoration Algorithm for the Minimization of Constrained Functions, Ordinary and Conjugate Gradient Version. Journal of Optimization Theory and Applications 4:213-246
21. E Polak (1997) Optimization: Algorithms and Consistent Approximations, Springer-Verlag, New York
22. RT Rockafellar. (1993) Lagrange multipliers and optimality. SIAM Review 35:183-238
23. JB Rosen (1961) The Gradient Projection Method for Nonlinear Programming, Part 2, Nonlinear Constraints. SIAM Journal on Applied Mathematics 9:514-532