Projected sequential quadratic programming methods

SIAM Journal on Optimization

Volumn 6, Issue 2, 1996, Pages 373-417

  Heinkenschloss, Matthias ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Bound constraints; Merit function; Optimal control; Projected newton methods; Sequential quadratic programming methods

Indexed keywords

EID: 0030303846     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/0806022     Document Type: Article

References (37)

1. W. ALT, The Lagrange Newton method for infinite dimensional optimization problems, Numer. Funct. Anal. Optim., 11 (1990), pp. 201-224.
2. D. P. BERTSEKAS, Projected Newton methods for optimization problems with simple constraints, SIAM J. Control Optim., 20 (1982), pp. 221-246.
3. J. T. BETTS AND P. D. FRANK, A sparse nonlinear optimization algorithm, Journal Optim. Theory Appl., 82 (1994), pp. 519-541.
4. P. T. BOGGS, J. W. TOLLE, AND A. J. KEARSLEY, A truncated SQP algorithm for large scale nonlinear programming problems, in Proc. Sixth Conference on Numerical Analysis and Optimization, S. Gomez and J.-P. Hennart, eds., Boston, 1994, Kluwer Academic Publishers, Norwell, MA.
5. J. BONNANS AND C. POLA, A trust region interior point algorithm for linearly constrained optimization, Tech. rep. 1948, INRIA, Domaine de Voluceau, 78153 Rocquencourt, France, 1993.
6. J. BURGER AND M. POGU, Functional and numerical solution of a control problem originating from heat transfer, J. Optim. Theory Appl., 68 (1991), pp. 49-73.
7. 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.
8. R. H. BYRD AND J. NOCEDAL, An analysis of reduced Hessian methods for constrained optimization, Math. Programming, 49 (1991), pp. 285-323.
9. T. F. COLEMAN AND J. LIU, An interior Newton method for quadratic programming, CTC93TR153, Center for Theory and Simulation in Science and Engineering, Cornell University, Ithaca, NY, 1993.
10. A. R. CONN, N. I. M. GOULD, AND P. L. TOINT, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal., 28 (1991), pp. 545-572.
11. E. J. CRAMER, J. E. DENNIS, JR., P. D. FRANK, R. M. LEWIS, AND G. R. SHUBIN, On alternative problem formulations for multidisciplinary design optimization, SIAM J. Optim., 4 (1994), pp. 754-776.
12. R. S. DEMBO AND U. TULOWITZKI, Sequential truncated quadratic programming, in Numerical Optimization 1984, P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1985, pp. 83-101.
13. J. E. DENNIS, JR. AND R. B. SCHNABEL, Numerical Methods for Nonlinear Equations and Unconstrained Optimization, Prentice-Hall, Englewood Cliffs, NJ, 1983.
14. M. EL-ALEM, A global convergence theory for the Celis-Dennis-Tapia trust region algorithm for constrained optimization, SIAM J. Numer. Anal., 28 (1991), pp. 266-290.
15. A. S. EL-BAKRY, R. A. TAPIA, T. TSUCHIYA, AND Y. ZHANG, On the formulation and theory of the primal-dual Newton interior-point method for nonlinear programming, TR92-40, Dept. of Computational & Applied Mathematics, Rice University, Houston, TX, 1992 (revised May 1993).
16. A. V. FIACCO AND G. P. MCCORMICK, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, New York, 1968.
17. R. FLETCHER, A class of methods for nonlinear programming with termination and convergence properties, in Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, 1970.
18. _, Practical Methods of Optimization, 2nd ed., John Wiley, New York, 1987.
19. A. FRIEDLANDER, J. M. MARTÍNEZ, AND S. A. SANDROS, On the resolution of linearly constrained convex minimization problems, SIAM J. Optim., 4 (1994), pp. 331-339.
20. J. C. GILBERT, On the local and global convergence of a reduced quasi-Newton method, Optimization, 20 (1989), pp. 421-450.
21. P. E. GILL, W. MURRAY, D. B. PONCELEÓN, AND M. A. SAUNDERS, Solving reduced KKT systems in barrier methods for linear and quadratic programming, Tech. report SOL 91 7, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, CA, 1991.
22. P. E. GILL, W. MURRAY, M. A. SAUNDERS, AND M. H. WRIGHT, Some theoretical properties of an augmented Lagrangian merit function, in Advances in Optimization and Parallel Computing, P. M. Pardalos, ed., Elsevier Science Publishers B.V., 1992, pp. 101-128.
23. C. T. KELLEY AND E. W. SACHS, Solution of optimal control problems by a pointwise projected Newton method, SIAM J. Control Optim., 33 (1995), pp. 1731-1757.
24. F.-S. KUPFER, An infinite-dimensional convergence theory for reduced SQP methods in Hilbert space, SIAM J. Optim., 6 (1996), pp. 126-163.
25. _, Reduced Successive Quadratic Programming in Hilbert Space with Applications to Optimal Control, Ph.D. thesis, Universität Trier, Fb-IV, Mathematik, D-54286 Trier, Germany, 1992.
26. F.-S. KUPFER AND E. W. SACHS, A prospective look at SQP methods for semilinear parabolic control problems, in Optimal Control of Partial Differential Equations, Irsee 1990, K.-H. Hoffmann and W. Krabs, eds., vol. 149, Springer Lect. Notes in Control and Information Sciences, 1991, pp. 143-157.
27. _, Numerical solution of a nonlinear parabolic control problem by a reduced SQP method, Comput. Optim. Appl., 1 (1992), pp. 113-135.
28. R. D. C. MONTEIRO, A globally convergent primal-dual interior point algorithm for convex programming, Math. Programming, 64 (1994), pp. 123-147.
29. W. MURRAY AND F. J. PRIETO, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590-640.
30. S. G. NASH AND A. SOFER, Algorithm 711: BTN: Software for parallel unconstrained optimization, ACM Trans. Math. Software, 18 (1992), pp. 414-448.
31. J. NOCEDAL AND M. L. OVERTON, Projected Hessian updating algorithms for nonlinearly constrained optimization, SIAM J. Numer. Anal., 22 (1985), pp. 821-850.
32. M. J. D. POWELL AND Y. YUAN, A trust region algorithm for equality constrained optimization, Math. Programming, 24 (1991), pp. 189-211.
33. K. SCHITTKOWSKI, The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search. Part 1: Convergence analysis, Numer. Math., 38 (1981), pp. 83-114.
34. M. H. WRIGHT, Interior point methods for constrained optimization, in Acta Numerica 1992, A. Iserles, ed., Cambridge University Press, Cambridge, 1992, pp. 341-407.
35. S. J. WRIGHT, An interior-point algorithm for linearly constrained optimization, SIAM J. Optim., 2 (1992), pp. 450-473.
36. Y. YE AND E. TSE, An extension of Karmarkar's protective algorithm for convex quadratic programming, Math. Programming, 44 (1989), pp. 157-179.
37. Y. ZHANG, R. A. TAPIA, AND F. POTRA, On the superlinear convergence of interior point algorithms for a general class of problems, SIAM J. Optim., 3 (1993), pp. 413-422.