國立虎尾科技大學 |

Face method = toward the new generation of linear programming /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Face method/ by Ping-Qi Pan.
其他題名:	toward the new generation of linear programming /
作者:	Pan, Ping-Qi.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xviii, 254 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Operations Research, Management Science. -
電子資源:	https://doi.org/10.1007/978-3-031-93594-7
ISBN:	9783031935947

Face method = toward the new generation of linear programming /
Pan, Ping-Qi.

Face methodtoward the new generation of linear programming /[electronic resource] :by Ping-Qi Pan. - Cham :Springer Nature Switzerland :2025. - xviii, 254 p. :ill., digital ;24 cm.

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.

The famous simplex method, invented by George B. Dantzig in 1947, moves from vertex to vertex in the underlying polyhedron until achieving an optimal vertex. As one of the most widely used mathematical tools, it has dominated the field of Linear Programming for nearly eighty years. However, it has exponential time complexity, and its performance turned out somehow unsatisfactory when solving some difficult LP problems since the solution process can sink into a degenerate vertex for too long. In 1984, Karmarkar published his work on the interior-point algorithm, which goes across the interior of the polyhedron, and which was not only of polynomial time complexity but also appeared fast. As such, it immediately drew the attention of researchers worldwide, giving rise to an upsurge in the interor-point method. Some scholars even considered it the winner against the simplex method for solving large-scale and sparse LP problems. However, the technique can only approach an optimal solution on the boundary, and it cannot be "warmly" started; hence, it is not applicable for solving integer LP problems, which form the primary domain of LP applications. The interior-point method failed to shake the domination of the simplex method. After years of research and exploration, the author proposes to break out of the simplex and interior-point methods. Over the recent years, the author has developed the so-called face method, which moves face by face to achieve an optimal face and solution. As the first book on the topic of face method, the monograph summarizes valuable findings and puts forward the theme to the academic world.

ISBN: 9783031935947

Standard No.: 10.1007/978-3-031-93594-7doiSubjects--Topical Terms:

785065
Operations Research, Management Science.

LC Class. No.: T57.74

Dewey Class. No.: 519.72

Face method = toward the new generation of linear programming /
LDR:03048nam a2200325 a 4500 001 1166631
003 DE-He213
005 20250830130152.0
006 m d
007 cr nn 008maaau
008 251217s2025 sz s 0 eng d
020 $a 9783031935947 $q (electronic bk.)
020 $a 9783031935930 $q (paper)
024 7 $a 10.1007/978-3-031-93594-7 $2 doi
035 $a 978-3-031-93594-7
040 $a GP $c GP
041 0 $a eng
050 4 $a T57.74
072 7 $a UYA $2 bicssc
072 7 $a COM014000 $2 bisacsh
072 7 $a UYA $2 thema
082 0 4 $a 519.72 $2 23
090 $a T57.74 $b .P187 2025
100 1 $a Pan, Ping-Qi. $3 1495422
245 1 0 $a Face method $h [electronic resource] : $b toward the new generation of linear programming / $c by Ping-Qi Pan.
260 $a Cham : $c 2025. $b Springer Nature Switzerland : $b Imprint: Springer,
300 $a xviii, 254 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a The famous simplex method, invented by George B. Dantzig in 1947, moves from vertex to vertex in the underlying polyhedron until achieving an optimal vertex. As one of the most widely used mathematical tools, it has dominated the field of Linear Programming for nearly eighty years. However, it has exponential time complexity, and its performance turned out somehow unsatisfactory when solving some difficult LP problems since the solution process can sink into a degenerate vertex for too long. In 1984, Karmarkar published his work on the interior-point algorithm, which goes across the interior of the polyhedron, and which was not only of polynomial time complexity but also appeared fast. As such, it immediately drew the attention of researchers worldwide, giving rise to an upsurge in the interor-point method. Some scholars even considered it the winner against the simplex method for solving large-scale and sparse LP problems. However, the technique can only approach an optimal solution on the boundary, and it cannot be "warmly" started; hence, it is not applicable for solving integer LP problems, which form the primary domain of LP applications. The interior-point method failed to shake the domination of the simplex method. After years of research and exploration, the author proposes to break out of the simplex and interior-point methods. Over the recent years, the author has developed the so-called face method, which moves face by face to achieve an optimal face and solution. As the first book on the topic of face method, the monograph summarizes valuable findings and puts forward the theme to the academic world.
650 2 4 $a Operations Research, Management Science. $3 785065
650 2 4 $a Programming Language. $3 1365750
650 2 4 $a Theory of Computation. $3 669322
650 2 4 $a Discrete Optimization. $3 1019327
650 2 4 $a Design and Analysis of Algorithms. $3 1365721
650 1 4 $a Computer Science Logic and Foundations of Programming. $3 1365757
650 0 $a Linear programming. $3 528157
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-93594-7
950 $a Professional and Applied Computing (SpringerNature-12059)