References
References
- Al-Mutairi D Grossmann C Vu KT 2000 Path-following barrier and penalty methods for linearly constrained problems Optimization 48 353 374 (extended version: Preprint MATH-NM-10-1998, TU Dresden)
- Anstreicher , KM and Vial , J-P . 1994 . On the convergence of an infeasible primal-dual interior-point method for convex programming . Optimization Methods and Software , 3 : 273 – 283 .
- Auslender , A . 1999 . Penalty and barrier methods: a unified framework . SIAM Journal on Optimization , 10 ( 1 ) : 211 – 230 .
- Burke , J and Song , Xu . 2002 . The complexity of a non-interior path following method for the linear complementarity problem . JOTA , 112 : 53 – 76 .
- Chen , B and Harker , PT . 1993 . A noninterior continuation method for quadratic and linear programming . SIAM Journal on Optimization , 3 : 503 – 515 .
- Cominetti , R and Dussault , J-P . 1994 . Stable exponential-penalty algorithm with superlinear convergence . Journal of Optimization Theory and Applications , 83 : 2, 285–309
- Cominetti , R and Pérez , JM . 1997 . Quadratic rate of convergence for a primal-dual exponential penalty algorithm . Optimization , 39 : 13 – 32 .
- Dussault , J-P . 1995 . Numerical stability and efficiency of Penalty algorithms . SIAM Journal on Numerical Analysis , 32 ( 1 ) : 296 – 317 .
- Felkel R 1996 An Interior-point Method for Large Scale QP Problems Preprint Nr.1850, TH Darmstadt
- Fiacco AV McCormick GP 1968 Nonlinear Programming: Sequential Unconstrained Minimization Techniques New York Wiley reprinted 2002
- Forsgren , A and Gill , PE . 1998 . Primal-dual interior methods for nonconvex nonlinear programming . SIAM Journal on Optimization , 8 ( 4 ) : 1132 – 1152 .
- Forsgren , A , Gill , PE and Wright , MH . 2002 . Interior methods for nonlinear optimization . SIAM Review , 44 ( 4 ) : 525 – 597 .
- Golub GH Van Loan CF 1983 Matrix Computations Baltimore North Oxford Academic
- Gould , N . 1998 . On the convergence of a sequential penalty function method for constrained minimization . SIAM Journal on Numerical Analysis , 26 : 107 – 128 .
- Gould , N , Orban , D , Sartenaer , A and Toint , PL . 2001 . Superlinear convergence of primal-dual interior point algorithms for nonlinear programming . SIAM Journal on Optimization , 11 ( 4 ) : 974 – 1002 .
- Grossmann , C . 1999 . Asymptotic analysis of a path-following barrier method for linearly constrained convex problems . Optimization , 45 : 69 – 87 .
- Grossmann , C . 2000 . Penalty/Barrier path-following in linearly constrained optimization, Discussiones Mathematicae, Differential Inclusions . Control and Optimization , 20 : 7 – 26 .
- Grossmann C Kaplan AA 1979 Straf-Barriere-Verfahren und modifizierte Lagrangefunktionen in der nichtlinearen Optmierung Teubner, Leipzig
- den Hertog , D , Jarre , F , Roos , C and Terlaky , T . 1995 . A sufficient condition for self-concordance, with application to some classes of structured convex programming problems . Mathematical Programming , 69 : 75 – 88 .
- Hlaváček I Haslinger J Nečas J Lovišek J 1988 Solution of Variational Inequalities in Mechanics Berlin Springer
- Hock W Schittkowski K 1981 Test Examples for Nonlinear Programming Codes (Berlin, Heidelberg, New York: Springer)
- Jarre F 1994 Interior-point Methods via Self-concordance or Relative Lipschitz Condition Universität Würzburg
- Kaplan AA Tichatschke R 2003 On Inexact Generalized Proximal Methods with Weak Error Tolerance Criterion Universität Trier
- Korzak , J . 2000 . Convergence analysis of inexact infeasible-interior-point algorithms for solving linear programming problems . SIAM Journal on Optimization , 11 ( 1 ) : 133 – 148 .
- Lootsma , FA . 1970 . Boundary properties of penalty functions for constrained minimization . Philips Res. Rept. Suppl , 3
- Mendel M 1998 Primal-duale Pfadorientierte Innere- und Äußere-Punkte-Verfahren zur Lösung linearer Optimierungsaufgaben Aachen Shaker
- Nash SG Sofer A 1998 Why extrapolation helps barrier methods Technical Report Operations Research and Engineering Department, George Mason University Virginia Fairfax
- Nesterov Y Nemirovskii A 1994 Interior-point Polynomial Algorithms in Convex Programming Philadelphia SIAM Publications
- Shanno , DF and Vanderbei , RJ . 2000 . Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods . Mathematical Programming , 87B : 303 – 316 .
- Schittkowski K 1987 More Test Examples for Nonlinear Programming Codes Berlin, Heidelberg, New York Springer
- Tits , AL , Wächter , A , Bakhtiari , S , Urban , TJ and Lawrence , CT . 2003 . A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties . SIAM Journal on Optimization , 14 ( 1 ) : 173 – 199 .
- Wierzbicki , AP . 1971 . A penalty function shifting method in constrained static optimization and its convergence properties . Arch. Autom. Telemech. , 16 : 395 – 416 .
- Wright , MH . 1995 . Why a pure primal Newton barrier step may be infeasible? . SIAM Journal on Optimization , 5 ( 1 ) : 1 – 12 .
- Wright , SJ . 2001 . On the convergence of the Newton/Log-barrier method . Mathematical Programming , 90A ( 1 ) : 71 – 100 .
- Wright , SJ . 2001 . Effects of finite-precision arithmetic on interior-point methods for nonlinear programming . SIAM Journal on Optimization , 12 ( 1 ) : 36 – 78 .
- Wright SJ 1997 Primal-Dual Interior-Point Methods Philadelphia SIAM Publications
- Ye Y 1997 Interior Point Algorithms: Theory and Analysis Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley and Sons)
- Zadlo M 2003 Weiterentwicklung von pfadverfolgenden Straf-/Barriereverfahren Diploma thesis, TU Dresden