Kebbiche, Zakia Linear complementarity problems solvable as linear programs. (English) Zbl 1463.90148 J. Numer. Anal. Approx. Theory 47, No. 2, 150-158 (2018). MSC: 90C05 90C33 PDFBibTeX XMLCite \textit{Z. Kebbiche}, J. Numer. Anal. Approx. Theory 47, No. 2, 150--158 (2018; Zbl 1463.90148)
Sierksma, Gerard; Zwols, Yori Linear and integer optimization. Theory and practice. 3rd ed. (English) Zbl 1329.90183 Advances in Applied Mathematics (Boca Raton). Boca Raton, FL: CRC Press (ISBN 978-1-4987-1016-9/hbk; 978-1-4987-1022-0/ebook). xxix, 656 p. (2015). Reviewer: Jaroslav Janáček (Žilina) MSC: 90C90 90-01 90C05 90C10 90C11 PDFBibTeX XMLCite \textit{G. Sierksma} and \textit{Y. Zwols}, Linear and integer optimization. Theory and practice. 3rd ed. Boca Raton, FL: CRC Press (2015; Zbl 1329.90183)
Sen, Syamal K.; Avila, Juan F. Parameter \(\alpha\) versus number of iterations in Karmarkar’s algorithm for LP. (English) Zbl 1216.65073 Neural Parallel Sci. Comput. 18, No. 3-4, 471-478 (2010). MSC: 65K05 90C05 PDFBibTeX XMLCite \textit{S. K. Sen} and \textit{J. F. Avila}, Neural Parallel Sci. Comput. 18, No. 3--4, 471--478 (2010; Zbl 1216.65073)
Nayak, R. K.; Biswal, M. P.; Padhy, S. Modification of Karmarkar’s projective scaling algorithm. (English) Zbl 1187.65068 Appl. Math. Comput. 216, No. 1, 227-235 (2010). MSC: 65K05 PDFBibTeX XMLCite \textit{R. K. Nayak} et al., Appl. Math. Comput. 216, No. 1, 227--235 (2010; Zbl 1187.65068) Full Text: DOI
Benterki, D.; Leulmi, A. An improving procedure of the interior projective method for linear programming. (English) Zbl 1143.65045 Appl. Math. Comput. 199, No. 2, 811-819 (2008). MSC: 65K05 90C05 90C51 PDFBibTeX XMLCite \textit{D. Benterki} and \textit{A. Leulmi}, Appl. Math. Comput. 199, No. 2, 811--819 (2008; Zbl 1143.65045) Full Text: DOI
Keraghel, A.; Kebbiche, Z.; Achache, M. An implementing weighted path-following algorithm for linear complementarity problems. (English) Zbl 1164.90030 An. Univ. Oradea, Fasc. Mat. 14, 53-64 (2007). Reviewer: Samir Kumar Neogy (New Delhi) MSC: 90C33 90C51 PDFBibTeX XMLCite \textit{A. Keraghel} et al., An. Univ. Oradea, Fasc. Mat. 14, 53--64 (2007; Zbl 1164.90030)
Naseri, Rasool; Valinejad, Azizollah An extended variant of Karmarkar’s interior point algorithm. (English) Zbl 1154.65338 Appl. Math. Comput. 184, No. 2, 737-742 (2007). MSC: 65K05 PDFBibTeX XMLCite \textit{R. Naseri} and \textit{A. Valinejad}, Appl. Math. Comput. 184, No. 2, 737--742 (2007; Zbl 1154.65338) Full Text: DOI
Lin, Chin-Tsai; Chen, Chie-Bein; Chen, Po-Ting On the modified interior point algorithm for solving multi-objective linear programming problems. (English) Zbl 1118.90047 Int. J. Inf. Manage. Sci. 17, No. 1, 107-127 (2006). MSC: 90C29 90C51 90C06 PDFBibTeX XMLCite \textit{C.-T. Lin} et al., Int. J. Inf. Manage. Sci. 17, No. 1, 107--127 (2006; Zbl 1118.90047)
Bonnans, J. Frédéric; Gilbert, J. Charles; Lemaréchal, Claude; Sagastizábal, Claudia A. Numerical optimization. Theoretical and practical aspects. Transl. from the French. 2nd reviseded. (English) Zbl 1108.65060 Universitext. Berlin: Springer (ISBN 3-540-35445-X/pbk). xiv, 490 p. (2006). Reviewer: Klaus Schittkowski (Bayreuth) MSC: 65K05 65-02 90-08 90C05 90C20 90C30 90C51 PDFBibTeX XMLCite \textit{J. F. Bonnans} et al., Numerical optimization. Theoretical and practical aspects. Transl. from the French. 2nd reviseded. Berlin: Springer (2006; Zbl 1108.65060) Full Text: DOI
Lakshmikantham, Vangipuram; Sen, Syamal K. Computational error and complexity in science and engineering. (English) Zbl 1076.65045 Mathematics in Science and Engineering 201. Amsterdam: Elsevier (ISBN 0-444-51860-6/hbk). ix, 248 p. (2005). Reviewer: Günter Mayer (Rostock) MSC: 65Gxx 68Qxx 65-02 68-02 65C05 00A06 65Fxx 65K05 65D25 65D32 65Y20 PDFBibTeX XMLCite \textit{V. Lakshmikantham} and \textit{S. K. Sen}, Computational error and complexity in science and engineering. Amsterdam: Elsevier (2005; Zbl 1076.65045) Full Text: Link
Bonnans, J. Frédéric; Gilbert, J. Charles; Lemaréchal, Claude; Sagastizábal, Claudia A. Numerical optimization. Theoretical and practical aspects. Transl. from the French. (English) Zbl 1014.65045 Universitext. Berlin: Springer. xiii, 419 p. (2003). Reviewer: Klaus Schittkowski (Bayreuth) MSC: 65K05 65-02 90-08 90C05 90C20 90C30 90C51 90C53 65Y15 65Y20 PDFBibTeX XMLCite \textit{J. F. Bonnans} et al., Numerical optimization. Theoretical and practical aspects. Transl. from the French. Berlin: Springer (2003; Zbl 1014.65045)
Xuan, Zhaocheng; Li, Xingsi; Sui, Yunkang Surrogate dual problem of quadratic programming and the algorithm. (English. Chinese original) Zbl 0965.90034 Chin. J. Numer. Math. Appl. 21, No. 1, 45-53 (1999); translation from J. Numer. Methods Comput. Appl. 19, No. 2, 144-152 (1998). MSC: 90C20 49M29 PDFBibTeX XMLCite \textit{Z. Xuan} et al., Chin. J. Numer. Math. Appl. 21, No. 1, 1 (1998; Zbl 0965.90034); translation from J. Numer. Methods Comput. Appl. 19, No. 2, 144--152 (1998)
Sherali, Hanif D.; Choi, Gyunghyun; Sen, Suvrajeet An exterior-point polytope sliding and deformation algorithm for linear programming problems. (English) Zbl 0906.90125 Informatica, Vilnius 8, No. 4, 559-582 (1997). MSC: 90C05 PDFBibTeX XMLCite \textit{H. D. Sherali} et al., Informatica, Vilnius 8, No. 4, 559--582 (1997; Zbl 0906.90125)
Guo, Tiande; Wu, Shiquan Properties of primal interior point methods for \(QP\). (English) Zbl 0867.90088 Optimization 37, No. 3, 227-238 (1996). MSC: 90C20 90C60 90C25 90-08 PDFBibTeX XMLCite \textit{T. Guo} and \textit{S. Wu}, Optimization 37, No. 3, 227--238 (1996; Zbl 0867.90088) Full Text: DOI
Jansen, B.; Roos, C.; Terlaky, T. Interior point methods, a decade after Karmarker. — A survey, with application to the smallest eigenvalue problem. (English) Zbl 0858.90095 Stat. Neerl. 50, No. 1, 146-170 (1996). MSC: 90C05 PDFBibTeX XMLCite \textit{B. Jansen} et al., Stat. Neerl. 50, No. 1, 146--170 (1996; Zbl 0858.90095) Full Text: DOI
Venkaiah, V. Ch. Deriving Karmarkar’s LP algorithm using angular projection matrix. (English) Zbl 0857.90086 Proc. Indian Acad. Sci., Math. Sci. 106, No. 1, 69-77 (1996). MSC: 90C05 65K05 PDFBibTeX XMLCite \textit{V. Ch. Venkaiah}, Proc. Indian Acad. Sci., Math. Sci. 106, No. 1, 69--77 (1996; Zbl 0857.90086) Full Text: DOI
Kapoor, Sanjiv; Vaidya, Pravin M. Speeding up Karmarkar’s algorithm for multicommodity flows. (English) Zbl 0848.90056 Math. Program. 73, No. 1 (A), 111-127 (1996). MSC: 90B10 90C05 PDFBibTeX XMLCite \textit{S. Kapoor} and \textit{P. M. Vaidya}, Math. Program. 73, No. 1 (A), 111--127 (1996; Zbl 0848.90056) Full Text: DOI
Arbel, Ami; Oren, Shmuel S. Using approximate gradients in developing an interactive interior primal-dual multiobjective linear programming algorithm. (English) Zbl 0908.90221 Eur. J. Oper. Res. 89, No. 1, 202-211 (1996). MSC: 90C29 90C05 90B50 PDFBibTeX XMLCite \textit{A. Arbel} and \textit{S. S. Oren}, Eur. J. Oper. Res. 89, No. 1, 202--211 (1996; Zbl 0908.90221) Full Text: DOI
Anstreicher, Kurt M. Potential reduction algorithms. (English) Zbl 0876.90066 Terlaky, Tamás (ed.), Interior point methods of mathematical programming. Dordrecht: Kluwer Academic Publishers. Appl. Optim. 5, 125-158 (1996). MSC: 90C05 PDFBibTeX XMLCite \textit{K. M. Anstreicher}, Appl. Optim. 5, 125--158 (1996; Zbl 0876.90066)
Singh, J. N.; Singh, D. Some remarks on the choice of step lengths in Karmarkar’s algorithm. (English) Zbl 0863.90112 Acta Cienc. Indica, Math. 21, No. 1, 53-58 (1995). MSC: 90C05 65K05 PDFBibTeX XMLCite \textit{J. N. Singh} and \textit{D. Singh}, Acta Cienc. Indica, Math. 21, No. 1, 53--58 (1995; Zbl 0863.90112)
Singh, J. N. Weighted least squares problem in the ellipsoid algorithm and projective method. (English) Zbl 0861.90098 Acta Cienc. Indica, Math. 21, No. 3, 383-385 (1995). MSC: 90C05 65K05 PDFBibTeX XMLCite \textit{J. N. Singh}, Acta Cienc. Indica, Math. 21, No. 3, 383--385 (1995; Zbl 0861.90098)
Singh, J. N.; Ranjan, Shashi; Singh, D. A modified termination rule for Karmarkar’s algorithm. (English) Zbl 0860.90089 J. Inf. Optim. Sci. 16, No. 3, 585-591 (1995). MSC: 90C05 PDFBibTeX XMLCite \textit{J. N. Singh} et al., J. Inf. Optim. Sci. 16, No. 3, 585--591 (1995; Zbl 0860.90089) Full Text: DOI
Karloff, Howard Linear programming. Repr. v. 1991. (English) Zbl 0925.90287 Basel: Birkhäuser. 152 p. (1995). MSC: 90C05 90-01 PDFBibTeX XMLCite \textit{H. Karloff}, Linear programming. Repr. v. 1991. Basel: Birkhäuser (1995; Zbl 0925.90287)
Arbel, Ami An interior multiple objective primal-dual linear programming algorithm using efficient anchoring points. (English) Zbl 0838.90103 J. Oper. Res. Soc. 46, No. 9, 1121-1132 (1995). MSC: 90C29 90C05 PDFBibTeX XMLCite \textit{A. Arbel}, J. Oper. Res. Soc. 46, No. 9, 1121--1132 (1995; Zbl 0838.90103) Full Text: DOI
Saigal, Romesh Linear programming: a modern integrated analysis. (English) Zbl 0856.90076 Dordrecht: Kluwer Academic Publishers. xi, 342 p. (1995). Reviewer: J.F.Bonnans (Le Chesnay) MSC: 90C05 90-01 65H10 90C25 PDFBibTeX XMLCite \textit{R. Saigal}, Linear programming: a modern integrated analysis. Dordrecht: Kluwer Academic Publishers (1995; Zbl 0856.90076)
Kalantari, Bahman A simple polynomial time algorithm for a convex hull problem equivalent to linear programming. (English) Zbl 0837.90085 Colbourn, Charles J. (ed.) et al., Combinatorics advances. Papers presented at the 25th annual Iranian mathematics conference, AIMC 25, held at Sharif University of Technology in Tehran, Iran, March 28-31, 1994. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 329, 207-216 (1995). Reviewer: J.Dénes (Budapest) MSC: 90C05 90C60 68Q25 PDFBibTeX XMLCite \textit{B. Kalantari}, Math. Appl., Dordr. 329, 207--216 (1995; Zbl 0837.90085)
Singh, J. N.; Singh, D. A variant of Karmarkar’s algorithm for linear programming. (English) Zbl 0860.90088 J. Bihar Math. Soc. 15(1992), 21-31 (1994). MSC: 90C05 PDFBibTeX XMLCite \textit{J. N. Singh} and \textit{D. Singh}, J. Bihar Math. Soc. 15, 21--31 (1994; Zbl 0860.90088)
Minoux, M. Probabilistic bounds on one step objective/potential function improvement in Karmarkar’s algorithm. (English) Zbl 0857.90084 RAIRO, Rech. Opér. 28, No. 4, 329-355 (1994). MSC: 90C05 PDFBibTeX XMLCite \textit{M. Minoux}, RAIRO, Rech. Opér. 28, No. 4, 329--355 (1994; Zbl 0857.90084) Full Text: DOI EuDML
Winston, Wayne L. Operations research. Applications and algorithms. 3rd ed. (English) Zbl 0867.90079 Andover, Hempshire: Duxbury Press. 1100 p. (1994). MSC: 90C05 90-01 90C10 90C30 90C35 91A05 90B50 90B05 90C40 90C15 90C39 90B22 60K25 90C31 PDFBibTeX XMLCite \textit{W. L. Winston}, Operations research. Applications and algorithms. 3rd ed. Andover, Hempshire: Duxbury Press (1994; Zbl 0867.90079)
Arbel, Ami; Oren, Shmuel S. A modification of Karmarkar’s algorithm to multiple objective linear programming problems. (English) Zbl 0817.90085 Tzeng, G. H. (ed.) et al., Multiple criteria decision making. Proceedings of the 10th international conference: Expand and enrich the domains of thinking and application, held at Taipei, Taiwan, July 19-24, 1992. New York: Springer-Verlag. 37-46 (1994). MSC: 90C29 90C05 PDFBibTeX XMLCite \textit{A. Arbel} and \textit{S. S. Oren}, in: Multiple criteria decision making. Proceedings of the 10th international conference: Expand and enrich the domains of thinking and application, held at Taipei, Taiwan, July 19-24, 1992. New York: Springer-Verlag. 37--46 (1994; Zbl 0817.90085)
Monteiro, Renato D. C. A globally convergent primal-dual interior point algorithm for convex programming. (English) Zbl 0820.90086 Math. Program. 64, No. 2 (A), 123-147 (1994). MSC: 90C25 90-08 PDFBibTeX XMLCite \textit{R. D. C. Monteiro}, Math. Program. 64, No. 2 (A), 123--147 (1994; Zbl 0820.90086) Full Text: DOI
Singh, J. N.; Singh, D. Convergence in Karmarkar’s algorithm: A review. (English) Zbl 0805.90075 Int. J. Math. Educ. Sci. Technol. 25, No. 3, 333-341 (1994). MSC: 90C05 PDFBibTeX XMLCite \textit{J. N. Singh} and \textit{D. Singh}, Int. J. Math. Educ. Sci. Technol. 25, No. 3, 333--341 (1994; Zbl 0805.90075) Full Text: DOI
Nakamura, Yoshimasa Lax pair and fixed point analysis of Karmarkar’s projective scaling trajectory for linear programming. (English) Zbl 0799.90088 Japan J. Ind. Appl. Math. 11, No. 1, 1-9 (1994). MSC: 90C05 93C10 PDFBibTeX XMLCite \textit{Y. Nakamura}, Japan J. Ind. Appl. Math. 11, No. 1, 1--9 (1994; Zbl 0799.90088) Full Text: DOI
Lustig, Irvin J.; Marsten, Roy E.; Shanno, David F. Interior point methods for linear programming: Computational state of the art. (English) Zbl 0798.90100 ORSA J. Comput. 6, No. 1, 1-14 (1994). MSC: 90C05 90C06 PDFBibTeX XMLCite \textit{I. J. Lustig} et al., ORSA J. Comput. 6, No. 1, 1--14 (1994; Zbl 0798.90100) Full Text: DOI
Faybusovich, Leonid E. On the phase portrait of the Karmarkar’s flow. (English) Zbl 0820.34029 Bowers, Kenneth L. (ed.) et al., Computation and control III. Proceedings of the third Bozeman conference, Bozeman, MT, USA, August 5-11, 1992. Boston, MA: Birkhäuser. Prog. Syst. Control Theory. 15, 203-210 (1993). Reviewer: A.L.Dontchev (Ann Arbor) MSC: 34D05 37C10 90C05 PDFBibTeX XMLCite \textit{L. E. Faybusovich}, in: Computation and control III. Proceedings of the third Bozeman conference, Bozeman, MT, USA, August 5-11, 1992. Boston, MA: Birkhäuser. 203--210 (1993; Zbl 0820.34029)
Arbel, A. Generating interior search directions for multiobjective linear programming using approximate gradients and efficient anchoring points. (English) Zbl 0818.90096 Optimization 28, No. 2, 149-164 (1993). MSC: 90C29 90C05 65F35 PDFBibTeX XMLCite \textit{A. Arbel}, Optimization 28, No. 2, 149--164 (1993; Zbl 0818.90096) Full Text: DOI
Powell, M. J. D. On the number of iterations of Karmarkar’s algorithm for linear programming. (English) Zbl 0804.90092 Math. Program. 62, No. 1 (B), 153-197 (1993). MSC: 90C05 90C60 PDFBibTeX XMLCite \textit{M. J. D. Powell}, Math. Program. 62, No. 1 (B), 153--197 (1993; Zbl 0804.90092) Full Text: DOI
Mitchell, J. E. Updating lower bounds when using Karmarkar’s projective algorithm for linear programming. (English) Zbl 0792.90044 J. Optimization Theory Appl. 78, No. 1, 127-142 (1993). MSC: 90C05 PDFBibTeX XMLCite \textit{J. E. Mitchell}, J. Optim. Theory Appl. 78, No. 1, 127--142 (1993; Zbl 0792.90044) Full Text: DOI
Powell, M. J. D. Log barrier methods for semi-infinite programming calculations. (English) Zbl 0801.65062 Lipitakis, Elias A. (ed.), Advances on computer mathematics and its applications. Papers presented at the first Hellenic conference on mathematics and informatics (HERMIS ’92) held at the Athens University of Economics, Athens, Greece, September 25-26, 1992. Singapore: World Scientific. 1-21 (1993). Reviewer: N.A.Warsi (Stone Mountain) MSC: 65K05 90C34 PDFBibTeX XMLCite \textit{M. J. D. Powell}, in: Advances on computer mathematics and its applications. Papers presented at the first Hellenic conference on mathematics and informatics (HERMIS '92) held at the Athens University of Economics, Athens, Greece, September 25-26, 1992. Singapore: World Scientific. 1--21 (1993; Zbl 0801.65062)
Anstreicher, Kurt M. Strict monotonicity and improved complexity in the standard form projective algorithm for linear programming. (English) Zbl 0795.90038 Math. Program. 62, No. 3 (A), 517-535 (1993). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{K. M. Anstreicher}, Math. Program. 62, No. 3 (A), 517--535 (1993; Zbl 0795.90038) Full Text: DOI
Gritzmann, Peter; Klee, Victor Mathematical programming and convex geometry. (English) Zbl 0806.90098 Gruber, P. M. (ed.) et al., Handbook of convex geometry. Volume A. Amsterdam: North-Holland. 627-674 (1993). Reviewer: P.Stavre (Craiova) MSC: 90C25 90C05 90-01 PDFBibTeX XMLCite \textit{P. Gritzmann} and \textit{V. Klee}, in: Handbook of convex geometry. Volume A. Amsterdam: North-Holland. 627--674 (1993; Zbl 0806.90098)
Anstreicher, Kurt M.; Watteyne, Patrick A family of search directions for Karmarkar’s algorithm. (English) Zbl 0782.90065 Oper. Res. 41, No. 4, 759-767 (1993). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{K. M. Anstreicher} and \textit{P. Watteyne}, Oper. Res. 41, No. 4, 759--767 (1993; Zbl 0782.90065) Full Text: DOI
Lagarias, J. C. A collinear scaling interpretation of Karmarkar’s linear programming algorithm. (English) Zbl 0791.65042 SIAM J. Optim. 3, No. 3, 630-636 (1993). Reviewer: S.Zabek (Lublin) MSC: 65K05 90C05 90C30 PDFBibTeX XMLCite \textit{J. C. Lagarias}, SIAM J. Optim. 3, No. 3, 630--636 (1993; Zbl 0791.65042) Full Text: DOI
Anstreicher, Kurt M.; Bosch, Robert A. Long steps in an \(O(n^ 3L)\) algorithm for linear programming. (English) Zbl 0783.90066 Math. Program., Ser. A 54, No. 3, 251-265 (1992). Reviewer: E.Duca (Cluj-Napoca) MSC: 90C05 90-08 90C60 65K05 PDFBibTeX XMLCite \textit{K. M. Anstreicher} and \textit{R. A. Bosch}, Math. Program. 54, No. 3 (A), 251--265 (1992; Zbl 0783.90066) Full Text: DOI
Monteiro, Renato D. C. On the continuous trajectories for a potential reduction algorithm for linear programming. (English) Zbl 0793.90032 Math. Oper. Res. 17, No. 1, 225-253 (1992). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{R. D. C. Monteiro}, Math. Oper. Res. 17, No. 1, 225--253 (1992; Zbl 0793.90032) Full Text: DOI
Mitchell, John E.; Todd, Michael J. Solving combinatorial optimization problems using Karmarkar’s algorithm. (English) Zbl 0763.90074 Math. Program. 56, No. 3 (A), 245-284 (1992). Reviewer: Ma Zhongfan (Beijing) MSC: 90C27 90C10 90C05 90-08 PDFBibTeX XMLCite \textit{J. E. Mitchell} and \textit{M. J. Todd}, Math. Program. 56, No. 3 (A), 245--284 (1992; Zbl 0763.90074) Full Text: DOI
Todd, Michael J. On Anstreicher’s combined phase I-phase II projective algorithm for linear programming. (English) Zbl 0773.90049 Math. Program. 55, No. 1 (A), 1-15 (1992). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{M. J. Todd}, Math. Program. 55, No. 1 (A), 1--15 (1992; Zbl 0773.90049) Full Text: DOI
Goffin, J. L.; Haurie, A.; Vial, J. P. Decomposition and nondifferentiable optimization with the projective algorithm. (English) Zbl 0762.90050 Manage. Sci. 38, No. 2, 284-302 (1992). Reviewer: H.Hollatz (Magdeburg) MSC: 90C05 90C30 90C25 90-08 PDFBibTeX XMLCite \textit{J. L. Goffin} et al., Manage. Sci. 38, No. 2, 284--302 (1992; Zbl 0762.90050) Full Text: DOI
Powell, M. J. D. The complexity of Karmarkar’s algorithm for linear programming. (English) Zbl 0809.65056 Griffiths, D. F. (ed.) et al., Numerical analysis 1991. Proceedings of the 14th Dundee conference, June 25-28, 1991, Dundee, UK. Dundee: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 260, 142-163 (1992). MSC: 65K05 90C05 65Y20 PDFBibTeX XMLCite \textit{M. J. D. Powell}, Pitman Res. Notes Math. Ser. 260, 142--163 (1992; Zbl 0809.65056)
Tachat, D. An optimal stopping criterion for the computation of an approximate projection in Karmarkar’s algorithm. (English) Zbl 0810.65060 Computational and applied mathematics, I. Algorithms and theory, Sel. Rev. Pap. IMACS 13th World Congr., Dublin/Irel. 1991, 453-461 (1992). Reviewer: I.Maros (Budapest) MSC: 65K05 90C35 PDFBibTeX XMLCite \textit{D. Tachat}, in: Computational and applied mathematics, I. Algorithms and theory. Selected and revised papers from the IMACS 13th world congress, Dublin, Ireland, July 1991. Proceedings. Amsterdam etc.: North-Holland. 453--461 (1992; Zbl 0810.65060)
Mehrotra, Sanjay; Sun, Jie A method of analytic centers for quadratically constrained convex quadratic programs. (English) Zbl 0742.65046 SIAM J. Numer. Anal. 28, No. 2, 529-544 (1991). Reviewer: T.F.Coleman (Ithaca) MSC: 65K05 90C20 65Y20 90C25 PDFBibTeX XMLCite \textit{S. Mehrotra} and \textit{J. Sun}, SIAM J. Numer. Anal. 28, No. 2, 529--544 (1991; Zbl 0742.65046) Full Text: DOI
Anstreicher, Kurt M. On the performance of Karmarkar’s algorithm over a sequence of iterations. (English) Zbl 0752.90044 SIAM J. Optim. 1, No. 1, 22-29 (1991). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{K. M. Anstreicher}, SIAM J. Optim. 1, No. 1, 22--29 (1991; Zbl 0752.90044) Full Text: DOI
Gonzaga, Clovis C. Large step path-following methods for linear programming. II: Potential reduction method. (English) Zbl 0754.90036 SIAM J. Optim. 1, No. 2, 280-292 (1991). MSC: 90C05 90-08 90C60 PDFBibTeX XMLCite \textit{C. C. Gonzaga}, SIAM J. Optim. 1, No. 2, 280--292 (1991; Zbl 0754.90036) Full Text: DOI
Karloff, Howard Linear programming. (English) Zbl 0748.90040 Progress in Theoretical Computer Science. Boston, MA etc., MA: Birkhäuser. viii, 142 p. (1991). Reviewer: M.A.Hanson (Tallahassee) MSC: 90C05 90-01 PDFBibTeX XMLCite \textit{H. Karloff}, Linear programming. Boston, MA: Birkhäuser (1991; Zbl 0748.90040)
Winston, Wayne L. Operations research applications and algorithms. 2nd. ed. (English) Zbl 0723.90048 Thomson Information/Publishing Group. International Student Edition. Boston, MA: PWS-Kent Publishing Company. xvi, 1262 p. £18.95 (1991). Reviewer: J.Preater (Keele) MSC: 90-01 90C05 90C10 90C30 90C35 91A05 90B50 90B05 90C40 90C15 90C39 90B22 60K25 90C31 PDFBibTeX XMLCite \textit{W. L. Winston}, Operations research applications and algorithms. 2nd. ed. Boston, MA: PWS-Kent Publishing Company (1991; Zbl 0723.90048)
Herzel, Stefano; Recchioni, Maria Cristina; Zirilli, Francesco A quadratically convergent method for linear programming. (English) Zbl 0731.65050 Linear Algebra Appl. 152, 255-289 (1991). Reviewer: S.Wright (Argonne) MSC: 65K05 65L05 90C05 65L20 34A34 PDFBibTeX XMLCite \textit{S. Herzel} et al., Linear Algebra Appl. 152, 255--289 (1991; Zbl 0731.65050) Full Text: DOI
Mladenović, Nenad; Petrić, Jovan Some properties of transportation manifold. (English) Zbl 0755.90061 Yugosl. J. Oper. Res. 1, No. 1, 65-69 (1991). Reviewer: M.Dalla Mora (L’Aquila) MSC: 90C08 90-08 PDFBibTeX XMLCite \textit{N. Mladenović} and \textit{J. Petrić}, Yugosl. J. Oper. Res. 1, No. 1, 65--69 (1991; Zbl 0755.90061)
Todd, Michael J. Probabilistic models for linear programming. (English) Zbl 0751.90056 Math. Oper. Res. 16, No. 4, 671-693 (1991). Reviewer: E.Trauwaert (Mol) MSC: 90C15 90C05 PDFBibTeX XMLCite \textit{M. J. Todd}, Math. Oper. Res. 16, No. 4, 671--693 (1991; Zbl 0751.90056) Full Text: DOI Link
Rajasekera, J. R.; Fang, S. C. On the convex programming approach to linear programming. (English) Zbl 0777.90028 Oper. Res. Lett. 10, No. 6, 309-312 (1991). MSC: 90C05 90C30 90C25 90-08 PDFBibTeX XMLCite \textit{J. R. Rajasekera} and \textit{S. C. Fang}, Oper. Res. Lett. 10, No. 6, 309--312 (1991; Zbl 0777.90028) Full Text: DOI
Kaliski, John A.; Ye, Yinyu Convergence behavior of Karmarkar’s projective algorithm for solving a simple linear program. (English) Zbl 0748.90039 Oper. Res. Lett. 10, No. 7, 389-393 (1991). Reviewer: V.D.Mazurov (Sverdlovsk) MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{J. A. Kaliski} and \textit{Y. Ye}, Oper. Res. Lett. 10, No. 7, 389--393 (1991; Zbl 0748.90039) Full Text: DOI
Gonzaga, Clovis C. Interior point algorithms for linear programming with inequality constraints. (English) Zbl 0744.90052 Math. Program., Ser. B 52, No. 2, 209-225 (1991). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{C. C. Gonzaga}, Math. Program. 52, No. 2 (B), 209--225 (1991; Zbl 0744.90052) Full Text: DOI
Calvillo Vives, Gilberto; López Mayo, Guillermo Polyhedral invariants and representative theorem in projective geometry. (English) Zbl 0737.90039 Advances in numerical partial differential equations and optimization, Proc. 5th Mex.-US Workshop, Mérida/Mex. 1989, 43-49 (1991). Reviewer: R.Nehse (Ilmenau) MSC: 90C05 52B12 51A05 PDFBibTeX XMLCite \textit{G. Calvillo Vives} and \textit{G. López Mayo}, in: An efficient linesearch for convex piecewise-linear/quadratic functions. . 43--49 (1991; Zbl 0737.90039)
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko An \(O(\sqrt n L)\) iteration potential reduction algorithm for linear complementarity problems. (English) Zbl 0738.90077 Math. Program., Ser. A 50, No. 3, 331-342 (1991). MSC: 90C33 90C60 90-08 PDFBibTeX XMLCite \textit{M. Kojima} et al., Math. Program. 50, No. 3 (A), 331--342 (1991; Zbl 0738.90077) Full Text: DOI
Bayer, D. A.; Lagarias, J. C. Karmarkar’s linear programming algorithm and Newton’s method. (English) Zbl 0736.90053 Math. Program., Ser. A 50, No. 3, 291-330 (1991). MSC: 90C05 49M15 65K05 90-08 90C30 PDFBibTeX XMLCite \textit{D. A. Bayer} and \textit{J. C. Lagarias}, Math. Program. 50, No. 3 (A), 291--330 (1991; Zbl 0736.90053) Full Text: DOI
Du, Dingzhu Convergence theory of feasible direction methods. (English) Zbl 0782.90088 Discrete Mathematics and Theoretical Computer Science. New York: Science Press New York, Ltd.. Beijing: Science Press. viii, 118 p. (1991). Reviewer: J.Abrham (Toronto) MSC: 90C30 90-02 PDFBibTeX XMLCite \textit{D. Du}, Convergence theory of feasible direction methods. New York: Science Press New York, Ltd.; Beijing: Science Press (1991; Zbl 0782.90088)
Singh, J. N.; Singh, D. A convergence result for Karmarkar’s algorithm for linear programming. (English) Zbl 0847.90102 J. Bihar Math. Soc. 13, 35-37 (1990). MSC: 90C05 PDFBibTeX XMLCite \textit{J. N. Singh} and \textit{D. Singh}, J. Bihar Math. Soc. 13, 35--37 (1990; Zbl 0847.90102)
Ye, Yinyu; Todd, Michael J. Containing and shrinking ellipsoids in the path-following algorithm. (English) Zbl 0746.90049 Math. Program., Ser. A 47, No. 1, 1-9 (1990). Reviewer: H.Tuy (Hanoi) MSC: 90C20 90C05 65K05 90C25 90C60 PDFBibTeX XMLCite \textit{Y. Ye} and \textit{M. J. Todd}, Math. Program. 47, No. 1 (A), 1--9 (1990; Zbl 0746.90049) Full Text: DOI
Bazaraa, Mokhtar S.; Jarvis, John J.; Sherali, Hanif D. Linear programming and network flows. 2nd ed. (English) Zbl 0722.90042 New York etc.: John Wiley & Sons. xiv, 684 p. £17.95 (1990). Reviewer: H.Noltemeier (Würzburg) MSC: 90C05 90B10 90-01 90C35 PDFBibTeX XMLCite \textit{M. S. Bazaraa} et al., Linear programming and network flows. 2nd ed. New York etc.: John Wiley \&| Sons (1990; Zbl 0722.90042)
Todd, Michael J. The effects of degeneracy and null and unbounded variables on variants of Karmarkar’s linear programming algorithm. (English) Zbl 0726.90054 Large-scale numerical optimization, Proc. Workshop, Ithaca/NY (USA) 1989, 81-91 (1990). MSC: 90C05 90-08 PDFBibTeX XML
Zhang, Xiangsun; Du, Dingzhu Extended binary search and its application in the design of polynomial- time algorithms for LP. (Chinese. English summary) Zbl 0726.90053 J. Syst. Sci. Math. Sci. 10, No. 4, 371-376 (1990). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{D. Du}, J. Syst. Sci. Math. Sci. 10, No. 4, 371--376 (1990; Zbl 0726.90053)
Karmarkar, Narendra An interior-point approach to NP-complete problems. I. (English) Zbl 0725.90075 Mathematical developments arising from linear programming, Proc. AMS-IMS- SIAM Jt. Summer Res. Conf., Brunswick/ME (USA) 1988, Contemp. Math. 114, 297-308 (1990). MSC: 90C20 90C10 90C60 90C09 90-08 65K05 PDFBibTeX XML
Monteiro, Renato D. C. Convergence and boundary behavior of the projective scaling trajectories for linear programming. (English) Zbl 0725.90062 Mathematical developments arising from linear programming, Proc. AMS-IMS- SIAM Jt. Summer Res. Conf., Brunswick/ME (USA) 1988, Contemp. Math. 114, 213-229 (1990). MSC: 90C05 90-08 PDFBibTeX XML
Mitchell, John E.; Todd, Michael J. Solving matching problems using Karmarkar’s algorithm. (English) Zbl 0725.90055 Mathematical developments arising from linear programming, Proc. AMS-IMS- SIAM Jt. Summer Res. Conf., Brunswick/ME (USA) 1988, Contemp. Math. 114, 309-318 (1990). MSC: 90C05 90C35 05C70 90-08 PDFBibTeX XML
Todd, Michael J. A Dantzig-Wolfe-like variant of Karmarkar’s interior-point linear programming algorithm. (English) Zbl 0724.90037 Oper. Res. 38, No. 6, 1006-1018 (1990). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{M. J. Todd}, Oper. Res. 38, No. 6, 1006--1018 (1990; Zbl 0724.90037) Full Text: DOI
Venkaiah, V. Ch. An efficient algorithm for linear programming. (English) Zbl 0718.90059 Proc. Indian Acad. Sci., Math. Sci. 100, No. 3, 295-301 (1990). MSC: 90C05 90-08 68W15 PDFBibTeX XMLCite \textit{V. Ch. Venkaiah}, Proc. Indian Acad. Sci., Math. Sci. 100, No. 3, 295--301 (1990; Zbl 0718.90059)
Douglas, Craig C.; Miranker, Willard L. Beyond massive parallelism: Numerical computation using associative tables. (English) Zbl 0716.65140 Parallel Comput. 16, No. 1, 1-25 (1990). Reviewer: W.Schönauer MSC: 65Y10 68Q10 65Y05 65L05 65M06 65K05 PDFBibTeX XMLCite \textit{C. C. Douglas} and \textit{W. L. Miranker}, Parallel Comput. 16, No. 1, 1--25 (1990; Zbl 0716.65140) Full Text: DOI
Mehrotra, Sanjay; Sun, Jie An algorithm for convex quadratic programming that requires \(O(n^{3,5}L)\) arithmetic operations. (English) Zbl 0714.90075 Math. Oper. Res. 15, No. 2, 342-363 (1990). Reviewer: A.Donescu MSC: 90C20 90C25 90C60 PDFBibTeX XMLCite \textit{S. Mehrotra} and \textit{J. Sun}, Math. Oper. Res. 15, No. 2, 342--363 (1990; Zbl 0714.90075) Full Text: DOI
Powell, M. J. D. Karmarkar’s algorithm: A view from nonlinear programming. (English) Zbl 0711.90052 Bull., Inst. Math. Appl. 26, No. 8-9, 165-181 (1990). MSC: 90C05 65K05 90C30 90-08 PDFBibTeX XMLCite \textit{M. J. D. Powell}, Bull., Inst. Math. Appl. 26, No. 8--9, 165--181 (1990; Zbl 0711.90052)
Ye, Yinyu Recovering optimal basic variables in Karmarkar’s polynomial algorithm for linear programming. (English) Zbl 0708.90048 Math. Oper. Res. 15, No. 3, 564-572 (1990). Reviewer: R.N.Kaul MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{Y. Ye}, Math. Oper. Res. 15, No. 3, 564--572 (1990; Zbl 0708.90048) Full Text: DOI
Oohori, Takahumi; Ohuchi, Azuma Symbolic generation of an optimal Karmarkar’s projective algorithm for sparse linear programs. (English) Zbl 0706.65059 System modelling and optimization, Proc. 14th IFIP Conf., Leipzig/GDR 1989, Lect. Notes Control Inf. Sci. 143, 194-203 (1990). Reviewer: J.Bonnans MSC: 65K05 90C05 90C06 68W30 PDFBibTeX XML
Lagarias, J. C. The nonlinear geometry of linear programming. III: Projective Legendre transform coordinates and Hilbert geometry. (English) Zbl 0699.90070 Trans. Am. Math. Soc. 320, No. 1, 193-225 (1990). Reviewer: E.Ederle MSC: 90C05 52B45 49M37 34A34 51K99 49M30 90C25 PDFBibTeX XMLCite \textit{J. C. Lagarias}, Trans. Am. Math. Soc. 320, No. 1, 193--225 (1990; Zbl 0699.90070) Full Text: DOI
Venkaiah, V. Ch. Computations in linear algebra: A new look at residue arithmetic. (English) Zbl 0698.65030 J. Indian Inst. Sci. 69, No. 6, 459-461 (1990). MSC: 65F30 68W30 65G50 65F15 PDFBibTeX XMLCite \textit{V. Ch. Venkaiah}, J. Indian Inst. Sci. 69, No. 6, 459--461 (1990; Zbl 0698.65030)
Kalantari, B. Karmarkar’s algorithm with improved steps. (English) Zbl 0695.90056 Math. Program., Ser. A 46, No. 1, 73-78 (1990). Reviewer: R.N.Kaul MSC: 90C05 65K05 PDFBibTeX XMLCite \textit{B. Kalantari}, Math. Program. 46, No. 1 (A), 73--78 (1990; Zbl 0695.90056) Full Text: DOI
Goffin, J. L.; Vial, J. P. Cutting planes and column generation techniques with the projective algorithm. (English) Zbl 0676.90041 J. Optimization Theory Appl. 65, No. 3, 409-429 (1990). Reviewer: J.L.Goffin MSC: 90C05 65K05 PDFBibTeX XMLCite \textit{J. L. Goffin} and \textit{J. P. Vial}, J. Optim. Theory Appl. 65, No. 3, 409--429 (1990; Zbl 0676.90041) Full Text: DOI
Adler, Ilan; Karmarkar, Narendra; Resende, Mauricio G. C.; Veiga, Geraldo Data structures and programming techniques for the implementation of Karmarkar’s algorithm. (English) Zbl 0752.90043 ORSA J. Comput. 1, No. 2, 84-106 (1989). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{I. Adler} et al., ORSA J. Comput. 1, No. 2, 84--106 (1989; Zbl 0752.90043) Full Text: DOI Link
Zhou, Jing; Xu, Nanrong; Chen, Weiyu Discussion on Karmarkar’s method for solving unstandard model. (English) Zbl 0705.90054 J. Southeast Univ., Engl. Ed. 5, No. 1, 38-45 (1989). MSC: 90C05 90C60 90-08 PDFBibTeX XMLCite \textit{J. Zhou} et al., J. Southeast Univ., Engl. Ed. 5, No. 1, 38--45 (1989; Zbl 0705.90054)
Tolla, Pierre Élaboration de logiciels efficaces utilisant l’algorithme de Karmarkar. (Elaboration of efficient software modules using Karmarkar’s algorithm). (French) Zbl 0688.90037 New methods in optimization and their industrial uses, Proc. Symp., Pau/Fr. and Paris/Fr. 1987, Int. Ser. Numer. Math. 87, 173-190 (1989). Reviewer: P.Tolla MSC: 90C05 65K05 90C06 PDFBibTeX XML
Adler, Ilan; Resende, Mauricio G. C.; Veiga, Geraldo; Karmarkar, Narendra An implementation of Karmarkar’s algorithm for linear programming. (English) Zbl 0682.90061 Math. Program., Ser. A 44, No. 3, 297-335 (1989). MSC: 90C05 65K05 PDFBibTeX XMLCite \textit{I. Adler} et al., Math. Program. 44, No. 3 (A), 297--335 (1989; Zbl 0682.90061) Full Text: DOI
Tseng, Paul A simple complexity proof for a polynomial-time linear programming algorithm. (English) Zbl 0682.90059 Oper. Res. Lett. 8, No. 3, 155-159 (1989). Reviewer: M.A.Hanson MSC: 90C05 68Q25 49M30 PDFBibTeX XMLCite \textit{P. Tseng}, Oper. Res. Lett. 8, No. 3, 155--159 (1989; Zbl 0682.90059) Full Text: DOI
Goldfarb, Donald; Mehrotra, Sanjay A self-correcting version of Karmarkar’s algorithm. (English) Zbl 0681.65042 SIAM J. Numer. Anal. 26, No. 4, 1006-1015 (1989). Reviewer: M.Vlach MSC: 65K05 90C05 90C32 PDFBibTeX XMLCite \textit{D. Goldfarb} and \textit{S. Mehrotra}, SIAM J. Numer. Anal. 26, No. 4, 1006--1015 (1989; Zbl 0681.65042) Full Text: DOI
Ye, Yinyu An extension of Karmarkar’s algorithm and the trust region method for quadratic programming. (English) Zbl 0678.90064 Progress in mathematical programming. Interior-point and related methods, Proc. Conf., Pacific Grove/Calif. 1987, 49-63 (1989). Reviewer: W.Breckner MSC: 90C20 65K05 PDFBibTeX XML
Vial, Jean-Philippe Approximate projections in a projective method for the linear feasibility problem. (English) Zbl 0677.90042 Progress in mathematical programming. Interior-point and related methods, Proc. Conf., Pacific Grove/Calif. 1987, 65-78 (1989). Reviewer: K.-H.Hoffmann MSC: 90C05 68Q25 PDFBibTeX XML
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko A polynomial-time algorithm for a class of linear complementarity problems. (English) Zbl 0676.90087 Math. Program., Ser. A 44, No. 1, 1-26 (1989). Reviewer: T.M.Liebling MSC: 90C33 68Q25 PDFBibTeX XMLCite \textit{M. Kojima} et al., Math. Program. 44, No. 1 (A), 1--26 (1989; Zbl 0676.90087) Full Text: DOI
Ye, Yinyu; Tse, Edison An extension of Karmarkar’s projective algorithm for convex quadratic programming. (English) Zbl 0674.90077 Math. Program., Ser. A 44, No. 2, 157-179 (1989). Reviewer: J.J.Dinkel MSC: 90C25 90C20 68Q25 90C05 65K05 PDFBibTeX XMLCite \textit{Y. Ye} and \textit{E. Tse}, Math. Program. 44, No. 2 (A), 157--179 (1989; Zbl 0674.90077) Full Text: DOI
Anstreicher, Kurt M. The worst-case step in Karmarkar’s algorithm. (English) Zbl 0674.90060 Math. Oper. Res. 14, No. 2, 294-302 (1989). Reviewer: P.Staniewski MSC: 90C05 90C06 65K05 PDFBibTeX XMLCite \textit{K. M. Anstreicher}, Math. Oper. Res. 14, No. 2, 294--302 (1989; Zbl 0674.90060) Full Text: DOI
Klincewicz, John G. Implementing an “exact” Newton method for separable convex transportation problems. (English) Zbl 0673.90086 Networks 19, No. 1, 95-105 (1989). Reviewer: J.-E.Martinez-Legaz MSC: 90C35 90B10 65K05 90C25 90C05 49M15 90C08 PDFBibTeX XMLCite \textit{J. G. Klincewicz}, Networks 19, No. 1, 95--105 (1989; Zbl 0673.90086) Full Text: DOI
Bayer, D. A.; Lagarias, J. C. The nonlinear geometry of linear programming. II: Legendre transform coordinates and central trajectories. (English) Zbl 0671.90046 Trans. Am. Math. Soc. 314, No. 2, 527-581 (1989). Reviewer: E.Ederle MSC: 90C05 52A40 34A34 PDFBibTeX XMLCite \textit{D. A. Bayer} and \textit{J. C. Lagarias}, Trans. Am. Math. Soc. 314, No. 2, 527--581 (1989; Zbl 0671.90046) Full Text: DOI
Bayer, D. A.; Lagarias, J. C. The nonlinear geometry of linear programming. I: Affine and projective scaling trajectories. (English) Zbl 0671.90045 Trans. Am. Math. Soc. 314, No. 2, 499-526 (1989). Reviewer: E.Ederle MSC: 90C05 52A40 34A34 PDFBibTeX XMLCite \textit{D. A. Bayer} and \textit{J. C. Lagarias}, Trans. Am. Math. Soc. 314, No. 2, 499--526 (1989; Zbl 0671.90045) Full Text: DOI
Mitchell, John E.; Todd, Michael J. A variant of Karmarkar’s linear programming algorithm for problems with some unrestricted variables. (English) Zbl 0667.65048 SIAM J. Matrix Anal. Appl. 10, No. 1, 30-38 (1989). Reviewer: R.Hettich MSC: 65K05 90C05 65F50 PDFBibTeX XMLCite \textit{J. E. Mitchell} and \textit{M. J. Todd}, SIAM J. Matrix Anal. Appl. 10, No. 1, 30--38 (1989; Zbl 0667.65048) Full Text: DOI
Anstreicher, Kurt M. A combined phase I-phase II projective algorithm for linear programming. (English) Zbl 0662.90048 Math. Program., Ser. A 43, No. 2, 209-223 (1989). Reviewer: V.S.Ishutkin MSC: 90C05 65K05 90C32 PDFBibTeX XMLCite \textit{K. M. Anstreicher}, Math. Program. 43, No. 2 (A), 209--223 (1989; Zbl 0662.90048) Full Text: DOI