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Theory and algorithms for linear optimization
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Linear Optimization (LO) is a widely taught and used mathematical technique that can also be applied to areas of science, commerce and industry. Because of advances in computer technology and developments in the field of interior point methods (IPM), problems that could not be solved years ago (because of lengthy time requirements) can now be solved in minutes by way of IPM approach to both the theory of LO and algorithms for LO (design, convergence, complexity and asymptotic behavior). Numerous exercises are provided to aid in understanding the material.
From the Publisher
Linear Optimization (LO) is a widely taught and used mathematical technique that can also be applied to areas of science, commerce and industry. Because of advances in computer technology and developments in the field of interior point methods (IPM), problems that could not be solved years ago (because of lengthy time requirements) can now be solved in minutes by way of IPM approach to both the theory of LO and algorithms for LO (design, convergence, complexity and asymptotic behavior). Numerous exercises are provided to aid in understanding the material.
A novel introduction to interior point algorithms
There has been a great interest in interior point algorithms since the publication of Karmarkar's seminal paper in 1984.This book dual "skew symmetric problem".This is certainly a novel introduction to interior point methods,not found in the literature. Part II is based on the usuallogarithmic barrier approach, more in tune with what is knownin the literature, and part III deals with a broader classof IPM's, some of which not based on "follow the centralpath" paradigm. Jim Renegar's famous short step algorithm findsits place here. Part IV is entitled "Miscellaneous Topics",and contains a short chapter on Karmakar's famous projectivealgorithm.My only complaint with the book is that since each of the fourparts attempt to be self contained, despite having considerableoverlap, the authors end up repeating the same thing a numberof times, at times annoying!. Anyway, this book is writtenby three of the foremost experts in the field of interior pointmethods, and if there is one person from whom I would want tolearn IPM's it is Prof. Tamas Terlaky. As the reviewer belowhas remarked check out his article on "An easy way to teachinterior point methods" too. To summarize, a extremelywell written book (the authors have put a lot of thoughtinto this!) and strongly recommended!.For other books on interior point methods one might wantto check out Wright's "Primal Dual Interior Point Methods",Ye's "Interior Point Algorithms", and finally BobVanderbei's book (the latter offers only a simpleintroduction!).
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