Primal-Dual Interior-Point Methods

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SIAM, 1997 - Technology & Engineering - 289 pages
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In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual 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 well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point 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 predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.
 

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Contents

OT54_ch1
1
OT54_ch2
21
OT54_ch3
49
OT54_ch4
65
OT54_ch5
83
OT54_ch6
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OT54_ch7
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OT54_ch8
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OT54_ch9
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OT54_ch10
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OT54_ch11
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OT54_appendixa
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OT54_appendixb
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OT54_backmatter
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