Vitor, Fabio; Easton, Todd Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming. (English) Zbl 1496.90033 Comput. Optim. Appl. 83, No. 1, 211-246 (2022). MSC: 90C05 90C51 PDFBibTeX XMLCite \textit{F. Vitor} and \textit{T. Easton}, Comput. Optim. Appl. 83, No. 1, 211--246 (2022; Zbl 1496.90033) Full Text: DOI
Barbara, Abdessamad An affine scaling method using a class of differential barrier functions: primal approach. (English) Zbl 1489.90212 Optimization 71, No. 6, 1443-1482 (2022). MSC: 90C51 65K05 90C05 90C46 PDFBibTeX XMLCite \textit{A. Barbara}, Optimization 71, No. 6, 1443--1482 (2022; Zbl 1489.90212) Full Text: DOI
Qian, Xun; Liao, Li-Zhi; Sun, Jie A strategy of global convergence for the affine scaling algorithm for convex semidefinite programming. (English) Zbl 1435.90103 Math. Program. 179, No. 1-2 (A), 1-19 (2020). MSC: 90C22 90C51 90C25 37C75 37N40 PDFBibTeX XMLCite \textit{X. Qian} et al., Math. Program. 179, No. 1--2 (A), 1--19 (2020; Zbl 1435.90103) Full Text: DOI
Morshed, Muhammad Sarowar; Noor-E-Alam, Muhammad Generalized affine scaling algorithms for linear programming problems. (English) Zbl 1458.90472 Comput. Oper. Res. 114, Article ID 104807, 17 p. (2020). MSC: 90C05 90-08 65K05 90C51 PDFBibTeX XMLCite \textit{M. S. Morshed} and \textit{M. Noor-E-Alam}, Comput. Oper. Res. 114, Article ID 104807, 17 p. (2020; Zbl 1458.90472) Full Text: DOI arXiv
Zorkal’tsev, V. I. Interior point method: history and prospects. (English. Russian original) Zbl 1432.90006 Comput. Math. Math. Phys. 59, No. 10, 1597-1612 (2019); translation from Zh. Vychisl. Mat. Mat. Fiz. 59, No. 10, 1649-1665 (2019). MSC: 90-03 01A60 01A65 90C51 PDFBibTeX XMLCite \textit{V. I. Zorkal'tsev}, Comput. Math. Math. Phys. 59, No. 10, 1597--1612 (2019; Zbl 1432.90006); translation from Zh. Vychisl. Mat. Mat. Fiz. 59, No. 10, 1649--1665 (2019) Full Text: DOI
Bomze, Immanuel M.; Mertikopoulos, Panayotis; Schachinger, Werner; Staudigl, Mathias Hessian barrier algorithms for linearly constrained optimization problems. (English) Zbl 1421.90164 SIAM J. Optim. 29, No. 3, 2100-2127 (2019). MSC: 90C51 90C30 90C25 90C26 PDFBibTeX XMLCite \textit{I. M. Bomze} et al., SIAM J. Optim. 29, No. 3, 2100--2127 (2019; Zbl 1421.90164) Full Text: DOI arXiv
Gu, Ran; Yuan, Ya Xiang A partial first-order affine-scaling method. (English) Zbl 1461.65153 Acta Math. Sin., Engl. Ser. 35, No. 1, 1-16 (2019). MSC: 65K05 90C30 90C51 PDFBibTeX XMLCite \textit{R. Gu} and \textit{Y. X. Yuan}, Acta Math. Sin., Engl. Ser. 35, No. 1, 1--16 (2019; Zbl 1461.65153) Full Text: DOI
Zorkal’tsev, V. I.; Mokryĭ, I. V. Interior point algorithms in linear optimization. (Russian, English) Zbl 1413.90176 Sib. Zh. Ind. Mat. 21, No. 1, 11-20 (2018); translation in J. Appl. Ind. Math. 12, No. 1, 191-199 (2018). MSC: 90C05 90C51 PDFBibTeX XMLCite \textit{V. I. Zorkal'tsev} and \textit{I. V. Mokryĭ}, Sib. Zh. Ind. Mat. 21, No. 1, 11--20 (2018; Zbl 1413.90176); translation in J. Appl. Ind. Math. 12, No. 1, 191--199 (2018) Full Text: DOI
Polyak, Roman Lagrangian transformation and interior ellipsoid methods in convex optimization. (English) Zbl 1330.90135 J. Optim. Theory Appl. 164, No. 3, 966-992 (2015). Reviewer: Igor V. Konnov (Kazan) MSC: 90C51 90C25 90C26 90C46 PDFBibTeX XMLCite \textit{R. Polyak}, J. Optim. Theory Appl. 164, No. 3, 966--992 (2015; Zbl 1330.90135) Full Text: DOI
Wang, Xiao; Yuan, Ya-Xiang A trust region method based on a new affine scaling technique for simple bounded optimization. (English) Zbl 1307.90174 Optim. Methods Softw. 28, No. 4, 871-888 (2013). MSC: 90C30 90C51 PDFBibTeX XMLCite \textit{X. Wang} and \textit{Y.-X. Yuan}, Optim. Methods Softw. 28, No. 4, 871--888 (2013; Zbl 1307.90174) Full Text: DOI
Pan, Ping-Qi An affine-scaling pivot algorithm for linear programming. (English) Zbl 1273.90120 Optimization 62, No. 4, 431-445 (2013). MSC: 90C05 PDFBibTeX XMLCite \textit{P.-Q. Pan}, Optimization 62, No. 4, 431--445 (2013; Zbl 1273.90120) Full Text: DOI
Wang, Xiao A trust region affine scaling method for bound constrained optimization. (English) Zbl 1268.65083 Acta Math. Sin., Engl. Ser. 29, No. 1, 159-182 (2013). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 65K05 90C30 90C51 PDFBibTeX XMLCite \textit{X. Wang}, Acta Math. Sin., Engl. Ser. 29, No. 1, 159--182 (2013; Zbl 1268.65083) Full Text: DOI
Balbo, Antonio Roberto; Da Silva Souza, Márcio Augusto; Baptista, Edméa Cássia; Nepomuceno, Leonardo Predictor-corrector primal-dual interior point method for solving economic dispatch problems: a postoptimization analysis. (English) Zbl 1264.90177 Math. Probl. Eng. 2012, Article ID 376546, 26 p. (2012). MSC: 90C51 90C90 90B30 65K05 PDFBibTeX XMLCite \textit{A. R. Balbo} et al., Math. Probl. Eng. 2012, Article ID 376546, 26 p. (2012; Zbl 1264.90177) Full Text: DOI
Zorkal’tsev, V. I. Dual interior point algorithms. (English. Russian original) Zbl 1229.90269 Russ. Math. 55, No. 4, 26-43 (2011); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2011, No. 4, 33-53 (2011). MSC: 90C51 90C05 PDFBibTeX XMLCite \textit{V. I. Zorkal'tsev}, Russ. Math. 55, No. 4, 26--43 (2011; Zbl 1229.90269); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2011, No. 4, 33--53 (2011) Full Text: DOI
Wang, Yong; Fang, Shu-Cherng; Lavery, John E. A compressed primal-dual method for generating bivariate cubic \(L_{1}\) splines. (English) Zbl 1110.65015 J. Comput. Appl. Math. 201, No. 1, 69-87 (2007). MSC: 65D07 65K05 90C25 41A15 90C51 PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Comput. Appl. Math. 201, No. 1, 69--87 (2007; Zbl 1110.65015) Full Text: DOI
Dax, Achiya The \(\ell_1\) solution of linear inequalities. (English) Zbl 1429.65122 Comput. Stat. Data Anal. 50, No. 1, 40-60 (2006). MSC: 65K05 90C05 62-08 PDFBibTeX XMLCite \textit{A. Dax}, Comput. Stat. Data Anal. 50, No. 1, 40--60 (2006; Zbl 1429.65122) Full Text: DOI
Tseng, Paul Convergence properties of Dikin’s affine scaling algorithm for nonconvex quadratic minimization. (English) Zbl 1066.90076 J. Glob. Optim. 30, No. 2-3, 285-300 (2004). MSC: 90C20 90C26 PDFBibTeX XMLCite \textit{P. Tseng}, J. Glob. Optim. 30, No. 2--3, 285--300 (2004; Zbl 1066.90076) Full Text: DOI
Singh, J. N.; Singh, D. Interior-point methods for linear programming: a review. (English) Zbl 1006.90088 Int. J. Math. Educ. Sci. Technol. 33, No. 3, 405-423 (2002). MSC: 90C51 90C05 90-02 PDFBibTeX XMLCite \textit{J. N. Singh} and \textit{D. Singh}, Int. J. Math. Educ. Sci. Technol. 33, No. 3, 405--423 (2002; Zbl 1006.90088) Full Text: DOI
Dax, Achiya Loss and retention of accuracy in affine scaling methods. (English) Zbl 1099.90592 Optim. Methods Softw. 15, No. 2, 121-151 (2001). MSC: 90C51 65K05 90C20 PDFBibTeX XMLCite \textit{A. Dax}, Optim. Methods Softw. 15, No. 2, 121--151 (2001; Zbl 1099.90592) Full Text: DOI
Dowling, Michael L. Affine scaling with degenerate linear programming problems. (English) Zbl 1017.90125 Optimization 49, No. 5-6, 477-494 (2001). MSC: 90C51 90C05 90C25 PDFBibTeX XMLCite \textit{M. L. Dowling}, Optimization 49, No. 5--6, 477--494 (2001; Zbl 1017.90125) Full Text: DOI
Pacelli, G.; Recchioni, M. C. Monotone variable-metric algorithm for linearly constrained nonlinear programming. (English) Zbl 0962.90045 J. Optimization Theory Appl. 104, No. 2, 255-279 (2000). MSC: 90C30 90C51 65K05 PDFBibTeX XMLCite \textit{G. Pacelli} and \textit{M. C. Recchioni}, J. Optim. Theory Appl. 104, No. 2, 255--279 (2000; Zbl 0962.90045) Full Text: DOI
Sheu, R. L. A generalized interior-point barrier function approach for smooth convex programming with linear constraints. (English) Zbl 0934.90057 J. Inf. Optim. Sci. 20, No. 2, 187-202 (1999). MSC: 90C25 PDFBibTeX XMLCite \textit{R. L. Sheu}, J. Inf. Optim. Sci. 20, No. 2, 187--202 (1999; Zbl 0934.90057) Full Text: DOI
Berkelaar, Arjan B.; Sturm, Jos F.; Zhang, Shuzhong Polynomial primal-dual cone affine scaling for semidefinite programming. (English) Zbl 0956.90025 Appl. Numer. Math. 29, No. 3, 317-333 (1999). MSC: 90C22 90C51 49M29 PDFBibTeX XMLCite \textit{A. B. Berkelaar} et al., Appl. Numer. Math. 29, No. 3, 317--333 (1999; Zbl 0956.90025) Full Text: DOI
Maros, István; Mészáros, Csaba The role of the augmented system in interior point methods. (English) Zbl 0943.90069 Eur. J. Oper. Res. 107, No. 3, 720-736 (1998). MSC: 90C51 PDFBibTeX XMLCite \textit{I. Maros} and \textit{C. Mészáros}, Eur. J. Oper. Res. 107, No. 3, 720--736 (1998; Zbl 0943.90069) Full Text: DOI
Muramatsu, Masakazu Affine scaling algorithm fails for semidefinite programming. (English) Zbl 0920.90099 Math. Program. 83, No. 3 (A), 393-406 (1998). MSC: 90C05 PDFBibTeX XMLCite \textit{M. Muramatsu}, Math. Program. 83, No. 3 (A), 393--406 (1998; Zbl 0920.90099) Full Text: DOI
Monteiro, Renato D. C.; Wang, Yanhui Trust region affine scaling algorithms for linearly constrained convex and concave programs. (English) Zbl 0901.90166 Math. Program. 80, No. 3 (A), 283-313 (1998). MSC: 90C30 PDFBibTeX XMLCite \textit{R. D. C. Monteiro} and \textit{Y. Wang}, Math. Program. 80, No. 3 (A), 283--313 (1998; Zbl 0901.90166) Full Text: DOI
Saigal, Romesh Matrix partitioning methods for interior point algorithms. (English) Zbl 1075.90559 Sādhanā 22, No. 4, 575-587 (1997). MSC: 90C51 65K05 90C05 PDFBibTeX XMLCite \textit{R. Saigal}, Sādhanā 22, No. 4, 575--587 (1997; Zbl 1075.90559) Full Text: DOI
Mitchell, John E. Fixing variables and generating classical cutting planes when using an interior point branch and cut method to solve integer programming problems. (English) Zbl 0923.90121 Eur. J. Oper. Res. 97, No. 1, 139-148 (1997). MSC: 90C10 PDFBibTeX XMLCite \textit{J. E. Mitchell}, Eur. J. Oper. Res. 97, No. 1, 139--148 (1997; Zbl 0923.90121) Full Text: DOI
Arbel, Ami An interior multiobjective primal-dual linear programming algorithm based on approximated gradients and efficient anchoring points. (English) Zbl 0889.90120 Comput. Oper. Res. 24, No. 4, 353-365 (1997). MSC: 90C29 PDFBibTeX XMLCite \textit{A. Arbel}, Comput. Oper. Res. 24, No. 4, 353--365 (1997; Zbl 0889.90120) Full Text: DOI
Dikin, I. I.; Roos, C. Convergence of the dual variables for the primal affine scaling method with unit steps in the homogeneous case. (English) Zbl 0892.90136 J. Optimization Theory Appl. 95, No. 2, 305-321 (1997). MSC: 90C05 PDFBibTeX XMLCite \textit{I. I. Dikin} and \textit{C. Roos}, J. Optim. Theory Appl. 95, No. 2, 305--321 (1997; Zbl 0892.90136) Full Text: DOI
Jansen, B.; Roos, C.; Terlaky, T.; Ye, Y. Improved complexity using higher-order correctors for primal-dual Dikin affine scaling. (English) Zbl 0884.90112 Math. Program. 76, No. 1 (B), 117-130 (1997). MSC: 90C05 90C60 90C33 PDFBibTeX XMLCite \textit{B. Jansen} et al., Math. Program. 76, No. 1 (B), 117--130 (1997; Zbl 0884.90112) Full Text: DOI
Tsuchiya, T.; Monteiro, R. D. C. Superlinear convergence of the affine scaling algorithm. (English) Zbl 0870.90083 Math. Program. 75, No. 1 (A), 77-110 (1996). MSC: 90C05 PDFBibTeX XMLCite \textit{T. Tsuchiya} and \textit{R. D. C. Monteiro}, Math. Program. 75, No. 1 (A), 77--110 (1996; Zbl 0870.90083) Full Text: DOI
Muramatsu, Masakazu; Tsuchiya, Takashi Convergence analysis of the projective scaling algorithm based on a long-step homogeneous affine scaling algorithm. (English) Zbl 0853.90084 Math. Program. 72, No. 3 (A), 291-305 (1996). MSC: 90C05 90C60 PDFBibTeX XMLCite \textit{M. Muramatsu} and \textit{T. Tsuchiya}, Math. Program. 72, No. 3 (A), 291--305 (1996; Zbl 0853.90084) Full Text: DOI
Saigal, Romesh The primal power affine scaling method. (English) Zbl 0848.90090 Ann. Oper. Res. 62, 375-417 (1996). MSC: 90C05 PDFBibTeX XMLCite \textit{R. Saigal}, Ann. Oper. Res. 62, 375--417 (1996; Zbl 0848.90090) Full Text: DOI
Sun, Jie A convergence analysis for a convex version of Dikin’s algorithm. (English) Zbl 0848.90101 Ann. Oper. Res. 62, 357-374 (1996). MSC: 90C25 PDFBibTeX XMLCite \textit{J. Sun}, Ann. Oper. Res. 62, 357--374 (1996; Zbl 0848.90101) Full Text: DOI
Muramatsu, Masakazu; Tsuchiya, Takashi An affine scaling method with an infeasible starting point: Convergence analysis under nondegeneracy assumption. (English) Zbl 0848.90088 Ann. Oper. Res. 62, 325-355 (1996). MSC: 90C05 PDFBibTeX XMLCite \textit{M. Muramatsu} and \textit{T. Tsuchiya}, Ann. Oper. Res. 62, 325--355 (1996; Zbl 0848.90088) Full Text: DOI
Saigal, Romesh A simple proof of a primal affine scaling method. (English) Zbl 0848.90089 Ann. Oper. Res. 62, 303-324 (1996). MSC: 90C05 PDFBibTeX XMLCite \textit{R. Saigal}, Ann. Oper. Res. 62, 303--324 (1996; Zbl 0848.90089) Full Text: DOI
Hwang, Tsung-Min; Lin, Chih-Hung; Lin, Wen-Wei A relaxed primal-dual path-following algorithm for linear programming. (English) Zbl 0848.90082 Ann. Oper. Res. 62, 173-196 (1996). MSC: 90C05 PDFBibTeX XMLCite \textit{T.-M. Hwang} et al., Ann. Oper. Res. 62, 173--196 (1996; Zbl 0848.90082) Full Text: DOI
Koenker, Roger; Park, Beum J. An interior point algorithm for nonlinear quantile regression. (English) Zbl 0855.62030 J. Econom. 71, No. 1-2, 265-283 (1996). MSC: 62G07 90C90 PDFBibTeX XMLCite \textit{R. Koenker} and \textit{B. J. Park}, J. Econom. 71, No. 1--2, 265--283 (1996; Zbl 0855.62030) 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
Arbel, Ami; Korhonen, Pekka Using aspiration levels in an interactive interior multiobjective linear programming algorithm. (English) Zbl 0908.90222 Eur. J. Oper. Res. 89, No. 1, 193-201 (1996). MSC: 90C29 90C05 PDFBibTeX XMLCite \textit{A. Arbel} and \textit{P. Korhonen}, Eur. J. Oper. Res. 89, No. 1, 193--201 (1996; Zbl 0908.90222) Full Text: DOI
Cheng, Z. Y.; Mitchell, J. E. A primal-dual interior-point method for linear programming based on a weighted barrier function. (English) Zbl 0839.90078 J. Optimization Theory Appl. 87, No. 2, 301-321 (1995). MSC: 90C05 PDFBibTeX XMLCite \textit{Z. Y. Cheng} and \textit{J. E. Mitchell}, J. Optim. Theory Appl. 87, No. 2, 301--321 (1995; Zbl 0839.90078) Full Text: DOI
Liao, A. Some variants of the Todd low-complexity algorithm. (English) Zbl 0842.90083 J. Optimization Theory Appl. 86, No. 1, 173-190 (1995). MSC: 90C05 PDFBibTeX XMLCite \textit{A. Liao}, J. Optim. Theory Appl. 86, No. 1, 173--190 (1995; Zbl 0842.90083) Full Text: DOI
Tsuchiya, T. Quadratic convergence of the Iri-Imai algorithm for degenerate linear programming problems. (English) Zbl 0840.90101 J. Optimization Theory Appl. 87, No. 3, 703-726 (1995). MSC: 90C05 PDFBibTeX XMLCite \textit{T. Tsuchiya}, J. Optim. Theory Appl. 87, No. 3, 703--726 (1995; Zbl 0840.90101) Full Text: DOI
Tsao, H.-S. Jacob; Fang, Shu-Cherng An unconstrained dual approach to solving Karmarkar-type linear programs using conventional barrier functions. (English) Zbl 0841.90093 ZOR, Math. Methods Oper. Res. 42, No. 3, 325-343 (1995). MSC: 90C05 PDFBibTeX XMLCite \textit{H. S. J. Tsao} and \textit{S.-C. Fang}, ZOR, Math. Methods Oper. Res. 42, No. 3, 325--343 (1995; Zbl 0841.90093) Full Text: DOI
Amaya, J. On the symmetric affine scaling algorithm for linear programming. (English) Zbl 0821.90080 Optimization 32, No. 2, 147-158 (1995). MSC: 90C05 49M30 PDFBibTeX XMLCite \textit{J. Amaya}, Optimization 32, No. 2, 147--158 (1995; Zbl 0821.90080) Full Text: DOI
Puthenpura, Sarat; Sinha, Lakshman; Fang, Shu-Cherng; Saigal, Romesh Solving stochastic programming problems via Kalman filter and affine scaling. (English) Zbl 0901.90155 Eur. J. Oper. Res. 83, No. 3, 503-513 (1995). MSC: 90C15 93E11 PDFBibTeX XMLCite \textit{S. Puthenpura} et al., Eur. J. Oper. Res. 83, No. 3, 503--513 (1995; Zbl 0901.90155) Full Text: DOI
Cheng, Zhao Yang; Mitchell, J. E. An alternative derivation of the projective interior point method for linear programming through the least squares approach. (English) Zbl 0820.90065 Optimization 31, No. 1, 95-106 (1994). MSC: 90C05 PDFBibTeX XMLCite \textit{Z. Y. Cheng} and \textit{J. E. Mitchell}, Optimization 31, No. 1, 95--106 (1994; Zbl 0820.90065) Full Text: DOI
Arbel, A. An interior multiobjective primal-dual linear programming algorithm using approximated gradients and sequential generation of anchor points. (English) Zbl 0818.90097 Optimization 30, No. 2, 137-150 (1994). MSC: 90C29 90C05 65F35 PDFBibTeX XMLCite \textit{A. Arbel}, Optimization 30, No. 2, 137--150 (1994; Zbl 0818.90097) Full Text: DOI
Todd, Michael J. Scaling, shifting and weighting in interior-point methods. (English) Zbl 0924.90112 Comput. Optim. Appl. 3, No. 4, 305-315 (1994). MSC: 90C05 PDFBibTeX XMLCite \textit{M. J. Todd}, Comput. Optim. Appl. 3, No. 4, 305--315 (1994; Zbl 0924.90112) Full Text: DOI
Evtushenko, Yuri G.; Zhadan, Vitali G. Stable barrier-projection and barrier-Newton methods in linear programming. (English) Zbl 0823.90084 Comput. Optim. Appl. 3, No. 4, 289-303 (1994). MSC: 90C05 PDFBibTeX XMLCite \textit{Y. G. Evtushenko} and \textit{V. G. Zhadan}, Comput. Optim. Appl. 3, No. 4, 289--303 (1994; Zbl 0823.90084) Full Text: DOI
Coleman, Thomas F.; Li, Yuying On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. (English) Zbl 0842.90106 Math. Program. 67, No. 2 (A), 189-224 (1994). Reviewer: M.Heinkenschloß (Trier) MSC: 90C30 PDFBibTeX XMLCite \textit{T. F. Coleman} and \textit{Y. Li}, Math. Program. 67, No. 2 (A), 189--224 (1994; Zbl 0842.90106) Full Text: DOI
Zhang, Shuzhong Convergence property of the Iri-Imai algorithm for some smooth convex programming problems. (English) Zbl 0819.90073 J. Optim. Theory Appl. 82, No. 1, 121-138 (1994). MSC: 90C25 90-08 90C51 PDFBibTeX XMLCite \textit{S. Zhang}, J. Optim. Theory Appl. 82, No. 1, 121--138 (1994; Zbl 0819.90073) Full Text: DOI
Todd, Michael J. Interior-point algorithms for semi-infinite programming. (English) Zbl 0831.90114 Math. Program. 65, No. 2 (A), 217-245 (1994). Reviewer: W.Krabs (Darmstadt) MSC: 90C34 65K05 PDFBibTeX XMLCite \textit{M. J. Todd}, Math. Program. 65, No. 2 (A), 217--245 (1994; Zbl 0831.90114) Full Text: DOI
Amaya, J. Numerical experiments with the symmetric affine scaling algorithm on degenerate linear programming problems. (English) Zbl 0818.90066 Optimization 27, No. 1-2, 51-62 (1993). MSC: 90C05 PDFBibTeX XMLCite \textit{J. Amaya}, Optimization 27, No. 1--2, 51--62 (1993; Zbl 0818.90066) Full Text: DOI
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
Mizuno, Shinji; Nagasawa, Atsushi A primal-dual affine-scaling potential-reduction algorithm for linear programming. (English) Zbl 0803.90090 Math. Program. 62, No. 1 (B), 119-131 (1993). Reviewer: D.I.Duca (Cluj-Napoca) MSC: 90C05 90C60 PDFBibTeX XMLCite \textit{S. Mizuno} and \textit{A. Nagasawa}, Math. Program. 62, No. 1 (B), 119--131 (1993; Zbl 0803.90090) Full Text: DOI
Ishihara, Tohru; Kojima, Masakazu On the big \({\mathcal M}\) in the affine scaling algorithm. (English) Zbl 0804.90088 Math. Program. 62, No. 1 (B), 85-93 (1993). MSC: 90C05 PDFBibTeX XMLCite \textit{T. Ishihara} and \textit{M. Kojima}, Math. Program. 62, No. 1 (B), 85--93 (1993; Zbl 0804.90088) Full Text: DOI
Tsuchiya, Takashi Global convergence of the affine scaling algorithm for primal degenerate strictly convex quadratic programming problems. (English) Zbl 0793.90055 Ann. Oper. Res. 46-47, No. 1-4, 509-539 (1993). MSC: 90C25 90C20 90-08 PDFBibTeX XMLCite \textit{T. Tsuchiya}, Ann. Oper. Res. 46--47, No. 1--4, 509--539 (1993; Zbl 0793.90055) Full Text: DOI
Monteiro, R. D. C.; Tsuchiya, T.; Wang, Y. A simplified global convergence proof of the affine scaling algorithm. (English) Zbl 0804.90091 Ann. Oper. Res. 46-47, No. 1-4, 443-482 (1993). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{R. D. C. Monteiro} et al., Ann. Oper. Res. 46--47, No. 1--4, 443--482 (1993; Zbl 0804.90091) Full Text: DOI
Güler, O.; den Hertog, D.; Roos, C.; Terlaky, T.; Tsuchiya, T. Degeneracy in interior point methods for linear programming: A survey. (English) Zbl 0785.90067 Ann. Oper. Res. 46-47, No. 1-4, 107-138 (1993). MSC: 90C05 90C31 PDFBibTeX XMLCite \textit{O. Güler} et al., Ann. Oper. Res. 46--47, No. 1--4, 107--138 (1993; Zbl 0785.90067) Full Text: DOI
Hochbaum, Dorit S.; Seshadri, Sridhar The empirical performance of a polynomial algorithm for constrained nonlinear optimization. (English) Zbl 0786.90066 Ann. Oper. Res. 43, No. 1-4, 229-248 (1993). MSC: 90C30 90-08 PDFBibTeX XMLCite \textit{D. S. Hochbaum} and \textit{S. Seshadri}, Ann. Oper. Res. 43, No. 1--4, 229--248 (1993; Zbl 0786.90066) Full Text: DOI
Arbel, Ami An interior multiobjective linear programming algorithm. (English) Zbl 0793.90061 Comput. Oper. Res. 20, No. 7, 723-735 (1993). Reviewer: Chen Guangya (Beijing) MSC: 90C29 90C05 90-08 PDFBibTeX XMLCite \textit{A. Arbel}, Comput. Oper. Res. 20, No. 7, 723--735 (1993; Zbl 0793.90061) Full Text: DOI
Hall, Leslie A.; Vanderbei, Robert J. Two-thirds is sharp for affine scaling. (English) Zbl 0794.90033 Oper. Res. Lett. 13, No. 4, 197-201 (1993). MSC: 90C05 PDFBibTeX XMLCite \textit{L. A. Hall} and \textit{R. J. Vanderbei}, Oper. Res. Lett. 13, No. 4, 197--201 (1993; Zbl 0794.90033) Full Text: DOI
Güler, Osman; Ye, Yinyu Convergence behavior of interior-point algorithms. (English) Zbl 0803.90087 Math. Program. 60, No. 2 (A), 215-228 (1993). Reviewer: Du Ding-Zhu (Minneapolis) MSC: 90C05 90C33 PDFBibTeX XMLCite \textit{O. Güler} and \textit{Y. Ye}, Math. Program. 60, No. 2 (A), 215--228 (1993; Zbl 0803.90087) Full Text: DOI
Sun, Jie A convergence proof for an affine-scaling algorithm for convex quadratic programming without nondegeneracy assumptions. (English) Zbl 0781.90073 Math. Program. 60, No. 1 (A), 69-79 (1993). MSC: 90C20 90C25 PDFBibTeX XMLCite \textit{J. Sun}, Math. Program. 60, No. 1 (A), 69--79 (1993; Zbl 0781.90073) Full Text: DOI
Hipolito, Alexander L. A weighted least squares study of robustness in interior point linear programming. (English) Zbl 0799.90081 Comput. Optim. Appl. 2, No. 1, 29-46 (1993). Reviewer: E.De Santis (L’Aquila) MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{A. L. Hipolito}, Comput. Optim. Appl. 2, No. 1, 29--46 (1993; Zbl 0799.90081) Full Text: DOI
Carpenter, Tamra J.; Shanno, David F. An interior point method for quadratic programs based on conjugate projected gradients. (English) Zbl 0778.90048 Comput. Optim. Appl. 2, No. 1, 5-28 (1993). MSC: 90C20 90-08 90C25 PDFBibTeX XMLCite \textit{T. J. Carpenter} and \textit{D. F. Shanno}, Comput. Optim. Appl. 2, No. 1, 5--28 (1993; Zbl 0778.90048) Full Text: DOI
Freund, Robert M. Projective transformations for interior-point algorithms, and a superlinearly convergent algorithm for the w-center problem. (English) Zbl 0792.90041 Math. Program. 58, No. 3 (A), 385-414 (1993). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{R. M. Freund}, Math. Program. 58, No. 3 (A), 385--414 (1993; Zbl 0792.90041) Full Text: DOI
Kojima, Masakazu; Megiddo, Nimrod; Mizuno, Shinji Theoretical convergence of large-step primal-dual interior point algorithms for linear programming. (English) Zbl 0780.90063 Math. Program. 59, No. 1 (A), 1-21 (1993). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{M. Kojima} et al., Math. Program. 59, No. 1 (A), 1--21 (1993; Zbl 0780.90063) Full Text: DOI
Vanderbei, Robert J.; Carpenter, Tamra J. Symmetric indefinite systems for interior point methods. (English) Zbl 0791.90033 Math. Program., Ser. A 58, No. 1, 1-32 (1993). MSC: 90C05 90C25 90C20 90-08 PDFBibTeX XMLCite \textit{R. J. Vanderbei} and \textit{T. J. Carpenter}, Math. Program. 58, No. 1 (A), 1--32 (1993; Zbl 0791.90033) Full Text: DOI
Coleman, Thomas F.; Li, Yuying A globally and quadratically convergent affine scaling method for linear \(l_ 1\) problems. (English) Zbl 0760.90069 Math. Program., Ser. A 56, No. 2, 189-222 (1992). Reviewer: K.-H.Küfer MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{T. F. Coleman} and \textit{Y. Li}, Math. Program. 56, No. 2 (A), 189--222 (1992; Zbl 0760.90069) Full Text: DOI
Betke, U.; Gritzmann, P. Projection algorithms for linear programming. (English) Zbl 0767.90043 Eur. J. Oper. Res. 60, No. 3, 287-295 (1992). Reviewer: P.Loridan (Rantigny) MSC: 90C05 90-08 65K05 PDFBibTeX XMLCite \textit{U. Betke} and \textit{P. Gritzmann}, Eur. J. Oper. Res. 60, No. 3, 287--295 (1992; Zbl 0767.90043) Full Text: DOI
Birge, John R.; Freund, Robert M.; Vanderbei, Robert Prior reduced fill-in in solving equations in interior point algorithms. (English) Zbl 0767.90044 Oper. Res. Lett. 11, No. 4, 195-198 (1992). MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{J. R. Birge} et al., Oper. Res. Lett. 11, No. 4, 195--198 (1992; Zbl 0767.90044) Full Text: DOI
Roos, C.; Vial, J.-Ph. A polynomial method of approximate centers for linear programming. (English) Zbl 0771.90067 Math. Program., Ser. A 54, No. 3, 295-305 (1992). Reviewer: P.d’Alessandro (Roma) MSC: 90C05 90-08 90C60 PDFBibTeX XMLCite \textit{C. Roos} and \textit{J. Ph. Vial}, Math. Program. 54, No. 3 (A), 295--305 (1992; Zbl 0771.90067) 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
Tseng, Paul; Luo, Zhi-Quan On the convergence of the affine-scaling algorithm. (English) Zbl 0762.90052 Math. Program. 56, No. 3 (A), 301-319 (1992). Reviewer: R.Nehse (Ilmenau) MSC: 90C05 90C35 90C60 90-08 PDFBibTeX XMLCite \textit{P. Tseng} and \textit{Z.-Q. Luo}, Math. Program. 56, No. 3 (A), 301--319 (1992; Zbl 0762.90052) Full Text: DOI
Ye, Yinyu On affine scaling algorithms for nonconvex quadratic programming. (English) Zbl 0767.90065 Math. Program. 56, No. 3 (A), 285-300 (1992). MSC: 90C26 90C20 90C60 90-08 PDFBibTeX XMLCite \textit{Y. Ye}, Math. Program. 56, No. 3 (A), 285--300 (1992; Zbl 0767.90065) 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
Sheu, R.-L.; Fang, S.-C. Insights into the interior-point methods. (English) Zbl 0763.90065 Z. Oper. Res. 36, No. 3, 227-257 (1992). Reviewer: Ma Zhongfan (Beijing) MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{R. L. Sheu} and \textit{S. C. Fang}, Z. Oper. Res. 36, No. 3, 227--257 (1992; Zbl 0763.90065) Full Text: DOI
Birge, J. R.; Holmes, D. F. Efficient solution of two-stage stochastic linear programs using interior point methods. (English) Zbl 0792.90051 Comput. Optim. Appl. 1, No. 3, 245-276 (1992). Reviewer: V.Kankova (Praha) MSC: 90C15 90C05 90-08 90C08 PDFBibTeX XMLCite \textit{J. R. Birge} and \textit{D. F. Holmes}, Comput. Optim. Appl. 1, No. 3, 245--276 (1992; Zbl 0792.90051) Full Text: DOI
Tapia, R. A.; Zhang, Yin An optimal-basis identification technique for interior-point linear programming algorithms. (English) Zbl 0737.65052 Linear Algebra Appl. 152, 343-363 (1991). Reviewer: Xu Chengxian (Xian) MSC: 65K05 90C05 PDFBibTeX XMLCite \textit{R. A. Tapia} and \textit{Y. Zhang}, Linear Algebra Appl. 152, 343--363 (1991; Zbl 0737.65052) Full Text: DOI
Ye, Yinyu An \(O(n^ 3L)\) potential reduction algorithm for linear programming. (English) Zbl 0734.90057 Math. Program., Ser. A 50, No. 2, 239-258 (1991). MSC: 90C05 90C60 90-08 PDFBibTeX XMLCite \textit{Y. Ye}, Math. Program. 50, No. 2 (A), 239--258 (1991; Zbl 0734.90057) Full Text: DOI
Todd, Michael J. The affine-scaling direction for linear programming is a limit of projective-scaling directions. (English) Zbl 0729.65041 Linear Algebra Appl. 152, 93-105 (1991). Reviewer: P.Stavre (Craiova) MSC: 65K05 90C05 PDFBibTeX XMLCite \textit{M. J. Todd}, Linear Algebra Appl. 152, 93--105 (1991; Zbl 0729.65041) Full Text: DOI Link
Anstreicher, Kurt M. On monotonicity in the scaled potential algorithm for linear programming. (English) Zbl 0728.65058 Linear Algebra Appl. 152, 223-232 (1991). Reviewer: J.Terno (Dresden) MSC: 65K05 90C05 PDFBibTeX XMLCite \textit{K. M. Anstreicher}, Linear Algebra Appl. 152, 223--232 (1991; Zbl 0728.65058) Full Text: DOI
Adler, Ilan; Monteiro, Renato D. C. Limiting behavior of the affine scaling continuous trajectories for linear programming problems. (English) Zbl 0719.90044 Math. Program., Ser. A 50, No. 1, 29-51 (1991). Reviewer: R.N.Kaul (Delhi) MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{I. Adler} and \textit{R. D. C. Monteiro}, Math. Program. 50, No. 1 (A), 29--51 (1991; Zbl 0719.90044) Full Text: DOI
Gonzaga, Clovis C. Search directions for interior linear-programming methods. (English) Zbl 0718.90064 Algorithmica 6, No. 2, 153-181 (1991). Reviewer: Z.Ma (Beijing) MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{C. C. Gonzaga}, Algorithmica 6, No. 2, 153--181 (1991; Zbl 0718.90064) Full Text: DOI
Christiansen, E.; Kortanek, K. O. Computation of the collapse state in limit analysis using the LP primal affine scaling algorithm. (English) Zbl 0713.73035 J. Comput. Appl. Math. 34, No. 1, 47-63 (1991). MSC: 74S30 74R20 74C99 74S05 90C05 PDFBibTeX XMLCite \textit{E. Christiansen} and \textit{K. O. Kortanek}, J. Comput. Appl. Math. 34, No. 1, 47--63 (1991; Zbl 0713.73035) Full Text: DOI
Kojima, Masakazu; Megiddo, Nimrod; Noma, Toshihito; Yoshise, Akiko A unified approach to interior point algorithms for linear complementarity problems: A summary. (English) Zbl 0745.90069 Oper. Res. Lett. 10, No. 5, 247-254 (1991). MSC: 90C33 90C05 90C20 PDFBibTeX XMLCite \textit{M. Kojima} et al., Oper. Res. Lett. 10, No. 5, 247--254 (1991; Zbl 0745.90069) Full Text: DOI
den Hertog, D.; Roos, C. A survey of search directions in interior point methods for linear programming. (English) Zbl 0739.90041 Math. Program., Ser. B 52, No. 3, 481-509 (1991). MSC: 90C05 90-08 90-02 PDFBibTeX XMLCite \textit{D. den Hertog} and \textit{C. Roos}, Math. Program. 52, No. 3 (B), 481--509 (1991; Zbl 0739.90041) Full Text: DOI
Ye, Yinyu Comparative analysis of affine scaling algorithms based on simplifying assumptions. (English) Zbl 0774.90057 Math. Program., Ser. B 52, No. 3, 405-414 (1991). Reviewer: U.Zimmermann (Braunschweig) MSC: 90C05 90-08 90C60 PDFBibTeX XMLCite \textit{Y. Ye}, Math. Program. 52, No. 3 (B), 405--414 (1991; Zbl 0774.90057) Full Text: DOI
Tsuchiya, Takashi Global convergence of the affine scaling methods for degenerate linear programming problems. (English) Zbl 0749.90051 Math. Program., Ser. B 52, No. 3, 377-404 (1991). MSC: 90C05 PDFBibTeX XMLCite \textit{T. Tsuchiya}, Math. Program. 52, No. 3 (B), 377--404 (1991; Zbl 0749.90051) Full Text: DOI
Jan, Gwo-Ming; Fang, Shu-Cherng A new variant of the primal affine scaling algorithm for linear programming. (English) Zbl 0742.90054 Optimization 22, No. 5, 681-715 (1991). Reviewer: Paolo d’Alessandro (Roma) MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{G.-M. Jan} and \textit{S.-C. Fang}, Optimization 22, No. 5, 681--715 (1991; Zbl 0742.90054) Full Text: DOI
Sagara, Nobuko; Fukushima, Masao A hybrid method for the nonlinear least squares problem with simple bounds. (English) Zbl 0742.65050 J. Comput. Appl. Math. 36, No. 2, 149-157 (1991). Reviewer: S.Zabek (Lublin) MSC: 65K05 90C30 90C06 90C20 90C25 PDFBibTeX XMLCite \textit{N. Sagara} and \textit{M. Fukushima}, J. Comput. Appl. Math. 36, No. 2, 149--157 (1991; Zbl 0742.65050) Full Text: DOI
Goldfarb, Donald; Xiao, Dong A primal projective interior point method for linear programming. (English) Zbl 0741.90046 Math. Program., Ser. A 51, No. 1, 17-43 (1991). Reviewer: J.Parida (Rourkela) MSC: 90C05 90-08 90C32 PDFBibTeX XMLCite \textit{D. Goldfarb} and \textit{D. Xiao}, Math. Program. 51, No. 1 (A), 17--43 (1991; Zbl 0741.90046) 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
Lustig, Irvin J. Feasibility issues in a primal-dual interior-point method for linear programming. (English) Zbl 0726.90050 Math. Program., Ser. A 49, No. 2, 145-162 (1990). Reviewer: J.Rohn (Praha) MSC: 90C05 90-08 65K05 PDFBibTeX XMLCite \textit{I. J. Lustig}, Math. Program. 49, No. 2 (A), 145--162 (1990; Zbl 0726.90050) Full Text: DOI
Shanno, David F.; Bagchi, Ansuman A unified view of interior point methods for linear programming. (English) Zbl 0726.90049 Ann. Oper. Res. 22, 55-70 (1990). Reviewer: Zhang Xian-sun (Beijing) MSC: 90C05 90-08 PDFBibTeX XMLCite \textit{D. F. Shanno} and \textit{A. Bagchi}, Ann. Oper. Res. 22, 55--70 (1990; Zbl 0726.90049) Full Text: DOI
Torabi, M. Decomposed block Cholesky factorization in the Karmarkar algorithm. Solving a class of super large LP problems. (English) Zbl 0701.90060 Comput. Math. Appl. 20, No. 2, 1-7 (1990). MSC: 90C05 90C06 90-08 PDFBibTeX XMLCite \textit{M. Torabi}, Comput. Math. Appl. 20, No. 2, 1--7 (1990; Zbl 0701.90060) Full Text: DOI
Asic, Miroslav D.; Kovacevic-Vujcic, Vera V.; Radosavljevic-Nikolic, Mirjana D. Asymptotic behaviour of Karmarkar’s method for linear programming. (English) Zbl 0697.90049 Math. Program., Ser. A 46, No. 2, 173-190 (1990). Reviewer: T.Rapcsák MSC: 90C05 65K05 PDFBibTeX XMLCite \textit{M. D. Asic} et al., Math. Program. 46, No. 2 (A), 173--190 (1990; Zbl 0697.90049) Full Text: DOI