Linear programming. Foundations and extensions. This is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, the book underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: -- The two-phase simplex method; -- The primal-dual simplex method; -- The path-following interior-point method; -- The homogeneous self-dual methods. In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book’s webpage: http://www.princeton.edu/-rvdb/LPbook/. Also, check the book’s webpage for new online instructional tools and exercises that have been added in the new edition. For a review of the 1996 edition, see Zbl 0874.90133.

References in zbMATH (referenced in 51 articles , 2 standard articles )

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  1. Cheng, Raymond; Xu, Yuesheng: Minimum norm interpolation in the (\ell_1(\mathbbN)) space (2021)
  2. Vanderbei, Robert J.: Linear programming. Foundations and extensions (2020)
  3. Huong, Dinh Cong; Sau, Nguyen Huu: Finite-time stability and stabilisation of singular discrete-time linear positive systems with time-varying delay (2019)
  4. Borgwardt, S.; De Loera, J. A.; Finhold, E.: The diameters of network-flow polytopes satisfy the Hirsch conjecture (2018)
  5. Brauer, Christoph; Lorenz, Dirk A.; Tillmann, Andreas M.: A primal-dual homotopy algorithm for (\ell_1)-minimization with (\ell_\infty)-constraints (2018)
  6. Nakharutai, Nawapon; Troffaes, Matthias C. M.; Caiado, Camila C. S.: Improved linear programming methods for checking avoiding sure loss (2018)
  7. Sau, Nguyen H.; Phat, Vu N.: LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback (2018)
  8. Thammawichai, Mason; Kerrigan, Eric C.: Energy-efficient real-time scheduling for two-type heterogeneous multiprocessors (2018)
  9. Keshvari, Abolfazl: A penalized method for multivariate concave least squares with application to productivity analysis (2017)
  10. Wang, Mengdi: Vanishing price of decentralization in large coordinative nonconvex optimization (2017)
  11. Hermosilla, Cristopher: Legendre transform and applications to finite and infinite optimization (2016)
  12. Vanderbei, Robert; Lin, Kevin; Liu, Han; Wang, Lie: Revisiting compressed sensing: exploiting the efficiency of simplex and sparsification methods (2016)
  13. Hoffmann, Jan; Shao, Zhong: Type-based amortized resource analysis with integers and arrays (2015)
  14. Liu, Xingwen: Stability analysis of a class of nonlinear positive switched systems with delays (2015)
  15. Rathinam, Muruhan: Moment growth bounds on continuous time Markov processes on non-negative integer lattices (2015)
  16. Weyerman, W. Samuel; Rai, Anurag; Warnick, Sean: Model approximation for batch flow shop scheduling with fixed batch sizes (2015)
  17. Blanco, Victor; Puerto, Justo; Ben Ali, Safae El Haj: A semidefinite programming approach for solving multiobjective linear programming (2014)
  18. Matolcsi, Máté; Ruzsa, Imre Z.: Difference sets and positive exponential sums. I: General properties (2014)
  19. Fábián, Csaba I.; Papp, Olga; Eretnek, Krisztián: Implementing the simplex method as a cutting-plane method, with a view to regularization (2013)
  20. Bentobache, Mohand; Bibi, Mohand Ouamer: A two-phase support method for solving linear programs: numerical experiments (2012)

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