Dynamic control of infeasibility in equality constrained optimization

SIAM Journal on Optimization

Volumn 19, Issue 3, 2008, Pages 1299-1325

  Bielschowsky, Roberto H ^a   Gomes, Francisco A M ^b  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Constrained optimization; Large scale optimization; Nonlinear programming

Indexed keywords

DYNAMIC CONTROLS; EQUALITY CONSTRAINTS; EQUALITY-CONSTRAINED OPTIMIZATION; LARGE-SCALE OPTIMIZATION; LOCAL CONVERGENCE; NONLINEAR PROGRAMMING PROBLEM;

CONVERGENCE OF NUMERICAL METHODS; CYLINDERS (SHAPES); DYNAMIC PROGRAMMING; NONLINEAR PROGRAMMING;

CONSTRAINED OPTIMIZATION;

EID: 69649084640     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/070679557     Document Type: Article

References (45)

1. J. Abadie and J. Carpentier, Some Numerical Experiments with the GRG Method for Nonlinear Programming, Paper HR7422, Électricité de France, Paris, 1967.
2. J. Abadie and J. Carpentier, Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints, in Optimization, R. Fletcher, ed., Academic Press, London, 1969, pp. 37-47.
3. P. R. Amestoy, T. A. Davis, and I. S. Duff, An approximate minimum degree ordering algorithm, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 886-905.
4. L. T. Biegler, J. Nocedal, and C. Schmid, A reduced Hessian method for large-scale constrained optimization, SIAM J. Optim., 5 (1995), pp. 314-347.
5. S. Bonettini, V. Ruggiero, and F. Tinti, On the solution of indefinite systems arising in nonlinear programming problems, Numer. Linear Algebra Appl., 14 (2007), pp. 807-831.
6. J. R. Bunch and L. Kaufman, Some stable methods for calculating inertia and solving symmetric indefinite linear systems, Math. Comp., 31 (1977), pp. 163-179.
7. R. H. Byrd, An example of irregular convergence in some constrained optimization methods that use the projected Hessian, Math. Program., 32 (1985), pp. 232-237.
8. R. H. Byrd, On the convergence of constrained optimization methods with accurate Hessian information on a subspace, SIAM J. Numer. Anal., 27 (1990), pp. 141-153.
9. R. H. Byrd, J. C. Gilbert, and J. Nocedal, A trust region method based on interior point techniques for nonlinear program., Math. Program., 89 (2000), pp. 149-186.
10. 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.
11. T. Coleman and A. R. Conn, Nonlinear programming via an exact penalty function: Asymptotic analysis, Math. Program., 24 (1982), pp. 123-136. (Pubitemid 13461143)
12. T. F. Coleman and A. R. Conn, On the local convergence of a quasi-Newton method for the nonlinear programming problem, SIAM J. Numer. Anal., 21 (1984), pp. 755-769.
13. A. R. Conn, N. I. M. Gould, and Ph. L. Toint, Trust-Region Methods, SIAM, Philadelphia, 2000.
14. J. E. Dennis, H. J. Martinez, and R. A. Tapia, Convergence theory for the structured BFGS secant method with application to nonlinear least squares, J. Optim. Theory Appl., 61 (1989), pp. 161-178.
15. J. E. Dennis and L. N. Vicente, On the convergence theory of trust-region-based algorithms for equality-constrained optimization, SIAM J. Optim., 7 (1997), pp. 927-950.
16. E. D. Dolan and J. J. More, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), pp. 201-213.
17. M. El-Alem, A global convergence theory for Dennis, El-Alem, and Maciel's class of trustregion algorithms for constrained optimization without assuming regularity, SIAM J. Optim., 9 (1999), pp. 965-990.
18. R. Fletcher, Practical Methods of Optimization, 2nd ed., John Wiley & Sons, Chichester, UK, 1987.
19. N. I. M. Gould, M. E. Hribar, and J. Nocedal, On the solution of equality constrained quadratic programming problems arising in optimization, SIAM J. Sci. Comput., 23 (2001), pp. 1376-1395.
20. N. I. M. Gould, D. Orban, and P. L. Toint, GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization, ACM Trans. Math. Software, 29 (2003), pp. 353-372.
21. N. I. M. Gould, D. Orban, and P. L. Toint, CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited, ACM Trans. Math. Software, 29 (2003), pp. 373-394.
22. F. A. M. Gomes, M. C. Maciel, and J. M. Martinez, Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters, Math. Program., 84 (1999), pp. 161-200.
23. M. Lalee, J. Nocedal, and T. Plantenga, On the implementation of an algorithm for large-scale equality constrained optimization, SIAM J. Optim., 8 (1998), pp. 682-706.
24. J. M. Martínez, A trust-region SLCP model algorithm for non-linear programming, in Foundations of Computational Mathematics, F. Cucker and M. Shub, eds., Springer-Verlag, Berlin, 1997, pp. 246-255.
25. J. M. Martínez, Two-phase model algorithm with global convergence for nonlinear programming, J. Optim. Theory Appl., 96 (1998), pp. 397-436.
26. J. M. Martínez, Inexact restoration method with Lagrangian tangent decrease and new merit function for nonlinear programming, J. Optim. Theory Appl., 111 (2001), pp. 39-58.
27. J. M. Martínez and E. A. Pilotta, Inexact restoration algorithm for constrained optimization, J. Optim. Theory Appl., 104 (2000), pp. 135-163.
28. J. M. Martínez and E. A. Pilotta, Inexact restoration methods for nonlinear programming: Advances and perspectives, in Optimization and Control with Applications, L. Qi, K. Teo, and X. Yang, eds., Springer-Verlag, New York, 2005, pp. 271-292.
29. A. Miele, H. Y. Huang, and J. C. Heideman, Sequential gradient-restoration algorithm for the minimization of constrained functions-ordinary and gradient versions, J. Optim. Theory Appl., 4 (1969), pp. 213-243.
30. A. Miele, A. V. Levy, and E. E. Cragg, Modifications and extensions of the conjugate gradient-restoration algorithm for mathematical programming problems, J. Optim. Theory Appl., 7 (1971), pp. 450-472.
31. J. J. Moré and D. J. Thuente, Line search algorithms with guaranteed sufficient decrease, ACM Trans. Math. Software, 20 (1994), pp. 286-307.
32. H. Mukai and E. Polak, On the use of approximations in algorithms for optimization problems with equality and inequality constraints, SIAM J. Numer. Anal., 15 (1978), pp. 674-693.
33. M. J. D. Powell, A hybrid method for nonlinear equations, in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed., Gordon and Breach, London, 1970, pp. 87-114.
34. M. J. D. Powell, The convergence of variable metric methods for nonlinearly constrained optimization calculations, in Nonlinear Programming, 3, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1978, pp. 27-63.
35. M. Rom and M. Avriel, Properties of the sequential gradient-restoration algorithm (SGRA). 1. Introduction and comparison with related methods, J. Optim. Theory Appl., 62 (1989), pp. 77-98.
36. M. Rom and M. Avriel, Properties of the sequential gradient-restoration algorithm (SGRA). 2. Convergence analysis, J. Optim. Theory Appl., 62 (1989), pp. 99-125.
37. J. B. Rosen, The gradient projection method for nonlinear programming. Part I. Linear constraints, SIAM J. Appl. Math., 8 (1960), pp. 181-217.
38. J. B. Rosen, The gradient projection method for nonlinear programming. Part II. Nonlinear constraints, SIAM J. Appl. Math., 9 (1961), pp. 514-532.
39. O. Schenk and K. Gärtner, On fast factorization pivoting methods for symmetric indefinite systems, Electron. Trans. Numer. Anal., 23 (2006), pp. 158-179.
40. T. Steihaug, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal., 20 (1983), pp. 626-637.
41. R. A. Tapia, Quasi-Newton methods for equality constrained optimization: Equivalence of existing methods and a new implementation, in Nonlinear Programming, 3, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1978, pp. 125-164.
42. Ph. L. Toint, Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, I. S. Duff, ed., Academic Press, London, 1981, pp. 57-88.
43. A. Wächter and L. T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), pp. 25-57.
44. P. Wolfe, Methods of nonlinear programming, in Recent Advances in Mathematical Programming, R. L. Graves and P. Wolfe, eds., McGraw-Hill, New York, 1963, pp. 67-86.
45. Y. Yuan, An only 2-step Q-superlinear convergence example for some algorithms that use reduced Hessian approximations, Math. Programming, 32 (1985), pp. 224-231.