Interior Point Methods of Mathematical Programming

1. Front Matter

   Pages i-xxi

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2. Linear Programming

   1. Front Matter

      Pages 1-1

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   2. Introduction to the Theory of Interior Point Methods

      • Benjamin Jansen, Cornelis Roos, Tamás Terlaky

      Pages 3-34

   3. Affine Scaling Algorithm

      • Takashi Tsuchiya

      Pages 35-82

   4. Target-Following Methods for Linear Programming

      • Benjamin Jansen, Cornelis Roos, Tamás Terlaky

      Pages 83-124

   5. Potential Reduction Algorithms

      • Kurt M. Anstreicher

      Pages 125-158

   6. Infeasible-Interior-Point Algorithms

      • Shinji Mizuno

      Pages 159-187

   7. Implementation of Interior-Point Methods for Large Scale Linear Programs

      • Erling D. Anderson, Jacek Gondzio, Csaba Mészáros, Xiaojie Xu

      Pages 189-252

3. Convex Programming

   1. Front Matter

      Pages 253-253

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   2. Interior-Point Methods for Classes of Convex Programs

      • Florian Jarre

      Pages 255-296

   3. Complementarity Problems

      • Akiko Yoshise

      Pages 297-367

   4. Semidefinite Programming

      • Motakuri V. Ramana, Panos M. Pardalos

      Pages 369-398

   5. Implementing Barrier Methods for Nonlinear Programming

      • David F. Shanno, Mark G. Breitfeld, Evangelia M. Simantiraki

      Pages 399-414

4. Applications, Extensions

   1. Front Matter

      Pages 415-415

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   2. Interior Point Methods for Combinatorial Optimization

      • John E. Mitchell

      Pages 417-466

   3. Interior Point Methods for Global Optimization

      • Panos M. Pardalos, Mauricio G. C. Resende

      Pages 467-500

   4. Interior Point Approaches for the VLSI Placement Problem

      • Anthony Vannelli, Andrew Kennings, Paulina Chin

      Pages 501-528

One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every­ body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro­ gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin­ cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob­ lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).

• algorithms
• combinatorial optimization
• complementarity
• complexity
• global optimization
• linear optimization
• Mathematica
• mathematical programming
• nonlinear optimization
• optimization
• Potential
• programming
• VLSI

• Delft University of Technology, The Netherlands

  Tamás Terlaky

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