Box constrained quadratic programming with proportioning and projections

SIAM Journal on Optimization

Volumn 7, Issue 3, 1997, Pages 871-887

  Dostál, Zdeněk ^a  

^a VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

Author keywords

Conjugate gradients; Inexact subproblem solution; Projected search; Quadratic programming

Indexed keywords

EID: 0031285901     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623494266250     Document Type: Article

References (20)

1. M. S. BAZARAA AND C. M. SHETTY, Nonlinear Programming, John Wiley, New York, 1979.
2. D. B. BERTSEKAS, Constrained Optimization and Lagrange Multipliers Methods, Academic Press, New York, 1982.
3. P. H. CALAMAI AND J. J. MORÉ, Projected gradient methods for linearly constrained problems, Math. Programming, 39 (1987), pp. 93-116.
4. G. CIMATTI, On a problem of the theory of lubrication governed by a variational inequality, Appl. Math. Optim., 3 (1977), pp. 227-242.
5. Z. DOSTÁL, Duality based domain decomposition for the solution of free boundary problems, J. Comput. Appl. Math., 63 (1995), pp. 203-208.
6. Z. DOSTÁL, Directions of large decrease and quadratic programming, in Software and Algorithms of Numerical Mathematics X, I. Marek, ed., Charles University, Prague, 1993, pp. 9-22.
7. R. GLOWINSKI, Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, Berlin, New York, 1984.
8. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, John Hopkins, London, 1989.
9. I. GUSTAFSSON, Modified incomplete cholesky methods, in Preconditioning Methods, D. J. Evans, ed., Gordon and Breach, New York, 1983.
10. W. HACKBUSCH AND H. D. MITTELMANN, On multigrid methods for variational inequalities, Numer. Math., 42 (1983), pp. 65-76.
11. J. HASLINGER AND P. NEITTAANMÄKI, Finite Element Approximation for Optimal Shape Design, John Wiley, Chichester, 1988.
12. M. R. HESTENES AND E. STIEFEL, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stand., 49 (1952), pp. 409-436.
13. J. J. JÚDICE AND F. M. PIRES, Direct methods for convex quadratic programs subject to box constraints, Investigación Operacional, 9 (1989), pp. 23-56.
14. A. KLARBRING, Quadratic programs in frictionless contact problems, Internat. J. Engrg. Sci., 24 (1986), pp. 1207-1217.
15. M. KOČVARA AND J. ZOWE, An iterative two-step algorithm for linear complementarity problems, Numer. Math., 68 (1994), pp. 95-106.
16. J. J. MORÉ AND G. TORALDO, On the solution of large quadratic programming problems with bound constraints, SIAM J. Optim., 1 (1991), pp. 93-113.
17. D. P. O'LEARY, A generalized conjugate gradient algorithm for solving a class of quadratic programming problems, Linear Algebra Appl., 34 (1980), pp. 371-399.
18. B. T. POLYAK, The conjugate gradient method in extremal problems, U.S.S.R Comput. Math. and Math. Phys., 9 (1969), pp. 94-112.
19. E. K. YANG AND J. W. TOLLE, A class of methods for solving large convex quadratic programs subject to box constraints, Math. Programming, 51 (1991), pp. 223-228.
20. I. ZHANG, R. 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.