Title
PrimalDual InteriorPoint Methods,Used
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In the past decade, primaldual algorithms have emerged as the most important and useful algorithms from the interiorpoint class. This book presents the major primaldual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and wellwritten work. The major primaldual algorithms covered in this book are pathfollowing algorithms (short and longstep, predictorcorrector), potentialreduction algorithms, and infeasibleinteriorpoint algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictorcorrector algorithm. Also treated are extensions of primaldual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.
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