Practical Bilevel Optimization

1. Front Matter

   Pages i-xii

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2. Mathematical Programming

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Jonathan F. Bard

      Pages 3-16

   3. Linear Programming

      • Jonathan F. Bard

      Pages 17-75

   4. Integer Programming

      • Jonathan F. Bard

      Pages 76-136

   5. Nonlinear Programming

      • Jonathan F. Bard

      Pages 137-192

3. Bilevel Programming

   1. Front Matter

      Pages 193-193

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   2. Linear Bilevel Programming: Continuous Variables

      • Jonathan F. Bard

      Pages 195-231

   3. Linear Bilevel Programming: Discrete Variables

      • Jonathan F. Bard

      Pages 232-268

   4. Convex Bilevel Programming

      • Jonathan F. Bard

      Pages 269-300

   5. General Bilevel Programming

      • Jonathan F. Bard

      Pages 301-360

   6. Heuristics

      • Jonathan F. Bard

      Pages 361-388

4. Applications

   1. Front Matter

      Pages 389-389

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   2. Transportation Network Design

      • Jonathan F. Bard

      Pages 391-413

   3. Production Planning with Inexact Customer Demand

      • Jonathan F. Bard

      Pages 414-427

   4. Determining Price Support Levels for Biofuel Crops

      • Jonathan F. Bard

      Pages 428-454

5. Back Matter

   Pages 455-476

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The use of optimization techniques has become integral to the design and analysis of most industrial and socio-economic systems. Great strides have been made recently in the solution of large-scale problems arising in such areas as production planning, airline scheduling, government regulation, and engineering design, to name a few. Analysts have found, however, that standard mathematical programming models are often inadequate in these situations because more than a single objective function and a single decision maker are involved. Multiple objective programming deals with the extension of optimization techniques to account for several objective functions, while game theory deals with the inter-personal dynamics surrounding conflict. Bilevel programming, the focus of this book, is in a narrow sense the combination of the two. It addresses the problern in which two decision makers, each with their individual objectives, act and react in a noncooperative, sequential manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense.

• Variable
• algorithm
• algorithms
• complexity
• game theory
• linear optimization
• management
• mathematical programming
• mathematics
• model
• network
• nonlinear optimization
• operations research
• optimization
• programming

• Graduate Program in Operations Research, Department of Mechanical Engineering, The University of Texas, Austin, USA

  Jonathan F. Bard

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