A New Technique for Inconsistent QP Problems in the SQP Method

Mathematical Methods of Operations Research

Volumn 47, Issue 3, 1998, Pages 355-400

  Spellucci, P ^a  

^a THD FB4 AG8 ^*  (Germany)

Author keywords

Nonlinear programming; Sequential quadratic programming; SQP method

Indexed keywords

EID: 0001059736     PISSN: 14322994     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01198402     Document Type: Article

References (47)

1. Burke JV (1989) A sequential quadratic programming algorithm for potentially infeasible mathematical programs. J. Math. Anal. Applies 139:319-351
2. Burke JV (1992) A robust trust region algorithm for constrained nonlinear programming problems. SIOPT 2:325-347
3. Burke JV (1991) An exact penalization viewpoint of constrained optimization. SIAM J. Control and Optimization 29:968-998
4. Burke JV, Han SP (1989) A robust sequential quadratic programming method. Math. Prog. 43:277-303
5. Byrd RH, Tapia RA, Zhang Y (1992) An SQP augmented Lagrangian BFGS algorithm for constrained optimization. SIOPT 2:210-241
6. Byrd RH, Nocedal J, Schnabel B (1994) Representations of quasi-Newton-matrices and their use in limited memory methods. Math. Prog. 63:129-156
7. Chamberlain RM (1979) Some examples of cycling in variable metric methods for constrained minimization. Math. Prog, 16:378-383
8. Chamberlain RM, Powell MDJ, Lemarechal C, Petersen HC (1982) The watchdog technique for forcing convergence in algorithms for constrained optimization. Math. Prog. Study 16:1-17
9. Clarke FH (1987) Optimization and nonsmooth analysis, John Wiley, New York
10. Conn AR, Sinclair JW Quadratic programming via a non-differentiable penalty function. Univ. of Waterloo Dept. of Combinatorics and Optimization report CORR 75/15
11. Daniel JW (1973) Stability of definite quadratic programs. Math. Prog. 5:41-53
12. Dembo RS (1976) A set of geometric programming test problems and their solutions. Math. Prog. 10:192-213
13. El-Alem MM (1995) Global convergence without the assumption of linear independence for a trust-region algorithm for constrained optimization. J.O.T.A. 87:563-577
14. Felkel R (1996) An interior point method for large scale QP problems. THD Mathematics Department Report 1850
15. Fletcher R (1982) A model algorithm for composite nondifferentiable optimization problems. Math. Prog. 17:67-76
16. Fletcher R (1987) Practical methods of optimization. 2nd ed, Wiley, Chicester-New York
17. Fletcher R (1981) Second order correction for nondifferentiable optimization. 85-114 in Lect. Notes on Math. 912, Springer, Berlin Heidelberg New York
18. 1 penalty method for nonlinear constraints. In: Boggs PT, Byrd RH, Schnabel RB (eds.) Numerical optimization, SIAM Publications, Philadelphia
19. Friedlander A, Martinez JM, Santos SA (1994) On the resolution of linearly constrained convex minimization problems. SIOPT 4:331-339
20. Gill PhE, Murray W (1978) Numerically stable methods for quadratic programming. Math. Prog. 14:349-372
21. Gill PhE, Murray W, Wright MH (1980) Practical methods of optimization. Acad. Press, New York
22. Gill PhE, Murray W, Saunders M, Wright MH (1992) Some theoretical properties of an augmented Lagrangian merit function. In: Pardalos PM (ed.) Advances in optimization and parallel computing, North Holland, Amsterdam, pp. 101-128
23. Gill PhE, Hammarling S, Murray W, Saunders M, Wright, MH (1986) Users guide for NPSOL (Version 4.0). Dept. O.R. Stanford Univ. Rep. SOL 86-2
24. Goldfarb D, Idnani A (1983) A numerically stable dual method for solving strictly convex quadratic programs. Math. Prog. 27:1-33
25. Gould NIM (1991) An algorithm for large scale quadratic programming. I.M.A.J. Numer. Anal. 11:299-323
26. Himmelblau DM (1972) Applied nonlinear programming. McGraw-Hill, New York
27. Hock W, Schittkowski K (1981) Test examples for nonlinear programming codes. Lect, Not. in Econ. and Math. Syst. 187, Springer, Berlin Heidelberg New York
28. Heinz J, Spellucci P (1994) A successful implementation of the Pantoja-Mayne SQP-method. Optimization Methods and Software 4:1-28
29. Kanzow C (1994) An unconstrained optimization technique for large-scale linearly constrained convex minimization problems. Computing 53:101-117
30. Lucidi S (1988) New results on a class of exact augmented Lagrangians. J.O.T.A. 58:259-282
31. Luenberger DG (1984) Introduction to linear and nonlinear programming. 2nd ed, Addison-Wesley, Menlo Park
32. Mayne DQ, Sahba M (1985) An efficient algorithm for solving inequalities, J.O.T.A. 45:407-423
33. Murty KG (1988) Linear complementarity, linear and nonlinear programming. Heldermann, Berlin
34. Nocedal J, Overton M (1985) Projected Hessian updating alogorithms for nonlinearly constrained optimization. SINUM 22:821-850
35. Nowak I (1988) Ein quadratisches Optimierungsproblem mit Schlupfvariablen für die SQP-Methode zur Lösung des allgemeinen nichtlinearen Optimierungsproblems. Diplomarbeit, TH Darmstadt
36. Mayne DQ, Pantoja JFA (1991) Exact penalty function algorithm with simple updating of the penalty parameter J.O.T.A. 69:441-467
37. Panier ER, Tits AL (1991) Avoiding the Maratos effect by means of a nomnonotone line search. I. general constrained problems. SINUM 28:1183-1195
38. Powell MJD (1978) A fast algorithm for nonlinearly constrained optimization calculations. Lecture Notes on Mathematics 630, Springer, Berlin Heidelberg New York, pp. 144-157
39. Sahba M (1987) Globally convergent algorithm for nonlinearly constrained optimization problems. J.O.T.A. 52:291-309
40. Schittkowski K (1981) The nonlinear programming method of Wilson, Han and Powell with an augmented Lagrangian type line search function IL An efficient implementation using linear least squares sub-problems. Num. Math. 38:115-127
41. Schittkowski K (1983) On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function. Optimization 14:197-216
42. Schittkowski K (1987) More testexamples for nonlinear programming codes. Lect, Not. in Econ. and Math. Syst. 282, Springer, Berlin Heidelberg New York
43. Spellucci P (1993) Numerische Verfahren der nichtlinearen Optimierung. Birkhäuser, Basel
44. Spellucci P (1993) A SQP method for general nonlinear programs using only equality constrained sub-problems. THD FB4 Preprint 1562, Submitted for publication
45. Spellucci P (1985) Sequential quadratic programming: Theory, implementation, problems. In: Beckmann MJ, Gaede KW, Ritter K, Schneeweiss H (eds.) Methods of Operation Research 53, Anton Hain, Meisenheim, pp. 183-213
46. Spellucci P donlp 2. Program and users guide available as donlp2.shar from netlib/opt/donlp2
47. Tone K (1983) Revision of constraint approximations in the successive QP-method for nonlinear programming problems. Math. Prog. 26:144-152