Open AccessBook
Linear Programming and Extensions
TLDR
This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.Abstract:
In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered."The author of this book was the main force in establishing a new mathematical discipline, and he has contributed to its further development at every stage and from every angle. This volume ... is a treasure trove for those who work in this field--teachers, students, and users alike. Its encyclopaedic coverage, due in part to collaboration with other experts, makes it an absolute must."--S. Vajda, Zentralblatt fYr Mathematik und ihre Grenzgebieteread more
Citations
More filters
Book
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
Journal ArticleDOI
A tutorial on support vector regression
TL;DR: This tutorial gives an overview of the basic ideas underlying Support Vector (SV) machines for function estimation, and includes a summary of currently used algorithms for training SV machines, covering both the quadratic programming part and advanced methods for dealing with large datasets.
Journal ArticleDOI
Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Journal ArticleDOI
A new polynomial-time algorithm for linear programming
TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).
Journal ArticleDOI
Atomic Decomposition by Basis Pursuit
TL;DR: This work gives examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution, and obtains reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.