Face Method: Toward the New Generation of Linear Programming
暫譯: 面向新一代線性規劃的面方法
Pan, Ping-Qi
- 出版商: Springer
- 出版日期: 2025-08-30
- 售價: $7,700
- 貴賓價: 9.5 折 $7,315
- 語言: 英文
- 頁數: 254
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031935934
- ISBN-13: 9783031935930
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相關分類:
工程數學 Engineering-mathematics
海外代購書籍(需單獨結帳)
商品描述
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.
商品描述(中文翻譯)
著名的單純形法（simplex method）由喬治·B·丹齊格（George B. Dantzig）於1947年發明，該方法在底層多面體（polyhedron）中從一個頂點移動到另一個頂點，直到達到最佳頂點。作為最廣泛使用的數學工具之一，它在線性規劃（Linear Programming）領域主導了近八十年。然而，它具有指數時間複雜度，並且在解決某些困難的線性規劃問題時，其性能表現不盡人意，因為解決過程可能會在一個退化頂點上停留過久。
1984年，卡馬克（Karmarkar）發表了他的內點法（interior-point algorithm）研究，該方法穿越多面體的內部，不僅具有多項式時間複雜度，且表現出快速的特性。因此，它立即引起了全球研究人員的關注，並引發了內點法的熱潮。一些學者甚至認為它在解決大規模和稀疏的線性規劃問題上勝過單純形法。然而，該技術只能在邊界上接近最佳解，且無法進行“熱啟動”（warmly started）；因此，它不適用於解決整數線性規劃問題，而整數線性規劃問題是線性規劃應用的主要領域。內點法未能動搖單純形法的主導地位。
經過多年的研究和探索，作者提出要突破單純形法和內點法。近年來，作者開發了所謂的面法（face method），該方法逐面移動以達到最佳面和解決方案。作為面法主題的第一本書，這本專著總結了寶貴的研究成果，並向學術界提出了這一主題。
作者簡介
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).
作者簡介(中文翻譯)
潘平奇是東南大學（中國）數學學院的教授及博士生導師。他曾擔任中國數學規劃學會的常務理事及中國運籌學會的常務理事。他於1986年至1987年擔任華盛頓大學的訪問學者，並於1987年至1988年擔任康奈爾大學的訪問科學家。他的研究興趣集中在數學規劃和運籌學，特別是大規模線性規劃。潘教授獲得了中國江蘇省優秀科技工作者的榮譽稱號。國際傳記中心將他提名為2012年全球百位頂尖科學家之一。他被列為著名數學家，並於2017年獲得《世界名人錄》頒發的終身成就獎。他是《線性規劃計算》（第一版和第二版）的作者，該書由Springer於2014年和2023年出版。
