Ping-Qi Pan is a Professor and PhD Supervisor at the School of Mathematics of Southeast University (China). He was a standing council member of the Mathematical Programming Society of China and the standing council member of the Operation Research Society of China. He was a Visiting Scholar at the University of Washington (1986–1987) and a Visiting Scientist at Cornell University (1987–1988). His research interest focuses on mathematical programming and operations research, especially large-scale linear programming. Prof. Pan has received the honorary title of Outstanding Scientific-Technical Worker of the Jiangsu Province of China. The International Biographical Centre nominated him as one of the Top 100 Scientists (2012). Listed as a Noteworthy Mathematician, he won the Lifetime Achievement Award by Who’s Who in the World (2017). He is the author of “Linear Programming Computation” (1st and 2nd ed.) published by Springer (2014, 2023).

• Preface.- Acknowledgments.- Notation.- Simplex Method: The State of the Art.- Face Algorithm.- Generalized Face Method.- Dual Face Method.- Generalized Dual Face Method.- Reduced Face Method.- Dual Reduced Face Method.- Face Method with Cholesky Factorization.- Dual Face Method with Cholesky Factorization.- Appendix: Empirical Evaluation of Face and Dual Face Methods with Cholesky Factorization.- References.

Ping-Qi Pan is a Professor and PhD Supervisor at the School of Mathematics of Southeast University (China). He was a standing council member of the Mathematical Programming Society of China and the standing council member of the Operation Research Society of China. He was a Visiting Scholar at the University of Washington (1986–1987) and a Visiting Scientist at Cornell University (1987–1988). His research interest focuses on mathematical programming and operations research, especially large-scale linear programming. Prof. Pan has received the honorary title of Outstanding Scientific-Technical Worker of the Jiangsu Province of China. The International Biographical Centre nominated him as one of the Top 100 Scientists (2012). Listed as a Noteworthy Mathematician, he won the Lifetime Achievement Award by Who’s Who in the World (2017). He is the author of “Linear Programming Computation” (1st and 2nd ed.) published by Springer (2014, 2023).

• Preface.- Acknowledgments.- Notation.- Simplex Method: The State of the Art.- Face Algorithm.- Generalized Face Method.- Dual Face Method.- Generalized Dual Face Method.- Reduced Face Method.- Dual Reduced Face Method.- Face Method with Cholesky Factorization.- Dual Face Method with Cholesky Factorization.- Appendix: Empirical Evaluation of Face and Dual Face Methods with Cholesky Factorization.- References.

Ping-Qi Pan is a Professor and PhD Supervisor at the School of Mathematics of Southeast University (China). He was a standing council member of the Mathematical Programming Society of China and the standing council member of the Operation Research Society of China. He was a Visiting Scholar at the University of Washington (1986–1987) and a Visiting Scientist at Cornell University (1987–1988). His research interest focuses on mathematical programming and operations research, especially large-scale linear programming. Prof. Pan has received the honorary title of Outstanding Scientific-Technical Worker of the Jiangsu Province of China. The International Biographical Centre nominated him as one of the Top 100 Scientists (2012). Listed as a Noteworthy Mathematician, he won the Lifetime Achievement Award by Who’s Who in the World (2017). He is the author of “Linear Programming Computation” (1st and 2nd ed.) published by Springer (2014, 2023).

• Preface.- Acknowledgments.- Notation.- Simplex Method: The State of the Art.- Face Algorithm.- Generalized Face Method.- Dual Face Method.- Generalized Dual Face Method.- Reduced Face Method.- Dual Reduced Face Method.- Face Method with Cholesky Factorization.- Dual Face Method with Cholesky Factorization.- Appendix: Empirical Evaluation of Face and Dual Face Methods with Cholesky Factorization.- References.