Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

Applied Mathematics and Computation

Volumn 200, Issue 2, 2008, Pages 529-536

  de Carvalho, Esdras Penêdo ^a   dos Santos, Anésio ^b   Ma, To Fu ^c  

^a STATE UNIVERSITY OF MARINGÁ   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

^c UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Augmented Lagrangian; Barrier method; Gradient methods; Nonlinear optimization; Optimal power flow

Indexed keywords

GRADIENT METHODS; PROBLEM SOLVING; VIRTUAL REALITY;

AUGMENTED LAGRANGIANS; BARRIER METHOD; NONLINEAR OPTIMIZATION; OPTIMAL POWER FLOW;

LAGRANGE MULTIPLIERS;

EID: 44649185809     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.11.025     Document Type: Article

References (20)

1. Abadie J., and Carpentier J. Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints. In: Fletcher R. (Ed). Optimization (Proceedings of a Symposium held at University of Keele, 1968) (1969), Academic Press, London 37-47
2. Adibi M.M., et al. Optimal transformer tap selection using modified barrier-augmented Lagrangian method. IEEE Transactions on Power Systems 18 (2003) 251-257
3. Bertsekas D.P. Constrained Optimization and Lagrange Multiplier Methods. Computer Science and Applied Mathematics (1982), Academic Press, New York
4. Carpentier J. Contribution a l'étude du dispatching économique. Bulletin de la Société Française des Électriciens 13 (1962) 431-447
5. G.R.M. Costa, K. Langona, D.A. Alves, A new approach to the solution of the optimal power flow problem based on the modified Newton's method associated to an augmented Lagrangian function, in: Proceedings of the International Conference on Power System Technology vol. 2, Beijing, 1988, pp. 909-913.
6. Dennis Jr. J.E., and Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Classics in Applied Mathematics 16 (1996), SIAM, Philadelphia
7. Dommel H.W., and Tinney W.F. Optimal power flow solutions. Transactions on Power Apparatus and Systems 87 (1968) 1866-1876
8. Fiacco A.V., and McCormick G.P. Nonlinear Programming. Sequential Unconstrained Minimization Techniques (1968), John Wiley, New York (Classics in Applied Mathematics 4, second edition, SIAM, Philadelphia, 1990)
9. Forsgren A., Gill P.E., and Wright M.H. Interior methods for nonlinear optimization. SIAM Reviews 44 (2002) 525-597
10. Hestenes M.R. Multiplier and gradient methods. Journal of Optimization Theory and Applications 4 (1969) 303-320
11. Lasdon L.S., Waren A.D., Jain A., and Ratner M. Design and testing of a generalized reduced gradient code for nonlinear programming. ACM Transactions on Mathematical Software 4 (1978) 34-50
12. Lasdon L.S., and Waren A.D. Large scale nonlinear programming. Computers and Chemical Engineering 7 (1983) 595-604
13. Momoh J.A., El-Hawary M.E., and Adapa R. A review of selected optimal power flow literature to 1993 part I: nonlinear and quadratic programming approaches. IEEE Transactions on Power Systems 14 (1999) 96-104
14. Momoh J.A., El-Hawary M.E., and Adapa R. A review of selected optimal power flow literature to 1993 part II: Newton, linear programming and interior points methods. IEEE Transactions on Power Systems 14 (1999) 105-111
15. Nocedal J., and Wright S.J. Numerical Optimization, Springer Series in Operations Research (1999), Springer-Verlag, New York
16. Powell M.J.D. A method for nonlinear constraints in minimization problems. In: Fletcher R. (Ed). Optimization (Proceedings of a Symposium held at University of Keele, 1968) (1969), Academic Press, London 283-298
17. Santos Jr. A., Deckmann S., and Soares S. A dual augmented Lagrangian approach for optimal power flow. IEEE Transactions on Power Systems 3 (1988) 1020-1025
18. Santos Jr. A., and da Costa G.R.M. Optimal-power-flow solution by Newton's method applied to an augmented Lagrangian function. IEE Proceedings - Generation, Transmission and Distribution 142 (1995) 33-36
19. Wolfe P. Methods of nonlinear programming. Recent Advances in Mathematical Programming (1963), McGraw-Hill, New York 67-86
20. Power Systems Test Case Archive, University of Washington. .