# Newton-KKT interior-point methods for indefinite quadratic programming

## Primary tabs

Bibliographic reference | Absil, Pierre-Antoine ; Tits, Andre L.. Newton-KKT interior-point methods for indefinite quadratic programming. In: Computational Optimization and Applications : an international journal, Vol. 36, no. 1, p. 5-41 (2007) |
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Permanent URL | http://hdl.handle.net/2078.1/37601 |

## References Provided by I4OC

- P.-A. Absil, C.G. Baker, and K.A. Gallivan, “A truncated-CG style method for symmetric generalized eigenvalue problems,” J. Comput. Appllied Math., vol. 189, nos. 1–2, pp. 274–285, 2006.
- J.F. Bonnans and M. Bouhtou, “The trust region affine interior point algorithm for convex and nonconvex quadratic programming,” RAIRO Rech. Opér., vol. 29, pp. 195–217, 1995.
- Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst (eds.), “Templates for the solution of algebraic eigenvalue problems: A practical guide,” Society for Industrial and Applied Mathematics, Philadelphia, 2000.
- R.H. Byrd, J.C. Gilbert, and J. Nocedal, “A trust region method based on interior point techniques for nonlinear programming,” Math. Program., vol. 89, pp. 149–185, 2000.
- J. F. Bonnans and C. Pola, “A trust region interior point algorithm for linearly constrained optimization,” SIAM J. Optim., vol. 7, no. 3, pp. 717–731, 1997.
- S. Bakhtiari and A.L. Tits, “A simple primal-dual feasible interior-point method for nonlinear programming with monotone descent,” Comput. Optim. Appl., vol. 25, pp. 17–38, 2003.
- A.R. Conn, N.I.M. Gould, and Ph. L. Toint, “Trust-region methods,” MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, and Math. Program. Soc. (MPS), Philadelphia, PA, 2000.
- T.F. Coleman and J. Liu, “An interior Newton method for quadratic programming,” Math. Program., vol. 85, pp. 491–523, 1999.
- I.I. Dikin, “Iterative solution of problems of linear and quadratic programming,” Sov. Math. Dokl., vol. 8, pp. 674–675, 1967.
- C. Dang and L. Xu, “A barrier function method for the nonconvex quadratic programming problem with box constraints,” J. Glob. Optim., vol. 18, no. 2, pp. 165–188, 2000.
- A.S. El-Bakry, R.A. Tapia, T. Tsuchiya, and Y. Zhang, “On the formulation and theory of the Newton interior-point method for nonlinear programming,” J. Opt. Theory Appl., vol. 89, pp. 507–541, 1996.
- A. Forsgren and P.E. Gill, “Primal-dual interior methods for nonconvex nonlinear programming,” SIAM J. Optim., vol. 8, no. 4, pp. 1132–1152, 1998.
- A. Forsgren, P. E. Gill, and M. H. Wright, “Interior methods for nonlinear optimization,” SIAM Rev., vol. 44, no. 4, pp. 525–597, 2002.
- A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques Wiley, New-York, 1968.
- D.M. Gay, M.L. Overton, and M. H. Wright, “A primal-dual interior method for nonconvex nonlinear programming,” Advances in Nonlinear Programming, Y. Yuan (ed.). Kluwer Academic Publisher, 1998, pp. 31–56.
- C. Grossmann and M. Zadlo, “A general class of penalty/barrier path-following Newton methods for nonlinear programming,” Optim., vol. 54, no. 2, pp. 161–190, 2005.
- J.N. Herskovits, “Développement d’une méthode numérique pour l’optimization non-linéaire,” Ph.D. thesis, Université Paris IX - Dauphine, Paris, France, January 1982.
- J.N. Herskovits, “A two-stage feasible directions algorithm for nonlinear constrained optimization,” Math. Program., vol. 36, no. 1, pp. 19–38, 1986.
- R.D.C. Monteiro and I. Adler, “Interior path following primal-dual algorithms. Part ii: Convex quadratic programming,” Math. Program., vol. 44, pp. 43–66, 1989.
- J.J. Moré and G. Toraldo, “Algorithms for bound constrained quadratic programming problems,” Numer. Math., vol. 55, no. 4, pp. 377–400, 1989.
- R.D.C. Monteiro and T. Tsuchiya, “Global convergence of the affine scaling algorithm for convex quadratic programming,” SIAM J. Optim., vol. 8, no. 1, pp. 26–58, 1998.
*Numerical Optimization*, ISBN:0387987932, 10.1007/b98874- E.R. Panier, A.L. Tits, and J.N. Herskovits, “A QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization,” SIAM J. Control Optim., vol. 26, no. 4, pp. 788–811, 1988.
- H.-D. Qi and L. Qi, “A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization,” SIAM J. Optim., vol. 11, no. 1, pp. 113–132, 2000.
- P. Tseng, “Convergence properties of Dikin’s affine scaling algorithm for nonconvex quadratic minimization,” J. Glob. Optim., vol. 30, no. 2, pp. 285–300, 2004.
- A.L. Tits, A. Wächter, S. Bakhtiari, T.J. Urban, and C.T. Lawrence, “A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties,” SIAM J. Optim., vol. 14, no. 1, pp. 173–199, 2003.
- P. Tseng and Y. Ye, “On some interior-point algorithms for nonconvex quadratic optimization,” Math. Program., vol. 93, no. 2, Ser. A, pp. 217–225, 2002.
- A.L. Tits and J.L. Zhou, “A simple, quadratically convergent algorithm for linear and convex quadratic programming,” in Large Scale Optimization: State of the Art, W.W. Hager, D.W. Hearn, and P.M. Pardalos (eds.), Kluwer Academic Publishers, pp. 411–427, 1994.
- R.J. Vanderbei and D.F. Shanno, “An interior-point algorithm for nonconvex nonlinear programming,” Comp. Optim. Appl., vol. 13, pp. 231–252, 1999.
- M. H. Wright, “Ill-conditioning and computational error in interior methods for nonlinear programming,” SIAM J. Optim., vol. 9, no. 1, pp. 84–111, 1998.
- H. Yamashita, “A globally convergent primal-dual interior point method for constrained optimization,” Optim. Meth. Softw., vol. 10, pp. 443–469, 1998.
- Y. Ye, “Interior algorithms for linear, quadratic, and linearly constrained convex programming,” Ph.D. thesis, Stanford University, 1987.
- Y. Ye, “An extension of Karmarkar’s algorithm and the trust region method for quadratic programming,” Progress in Mathematical Programming (Pacific Grove, CA, 1987). Springer, New York, 1989, pp. 49–63.
- Y. Ye, “On affine scaling algorithms for nonconvex quadratic programming,” Math. Program., vol. 56, pp. 285–300, 1992.
- Y. Ye, “On the complexity of approximating a KKT point of quadratic programming,” Math. Program., vol. 80, pp. 195–211, 1998.
- Y.-F. Yang, D.-H. Li, and L. Qi, “A feasible sequential linear equation method for inequality constrained optimization,” SIAM J. Optim., vol. 13, no. 4, pp. 1222–1244, 2003.
- Y. Ye and E. Tse, “An extension of Karmarkar’s projective algorithm for convex quadratic programming,” Math. Program., vol. 44, no. 2 (Ser. A), pp. 157–179, 1989.