Computing Methods in Optimization Problems

Proceedings of a Conference Held at University of California, Los Angeles January 30-31, 1964

A. V. Balakrishnan, Lucien W. Neustadt

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9781483198125
• eBook ISBN:
  9781483223155
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Computing Methods in Optimization Problems deals with hybrid computing methods and optimization techniques using computers. One paper discusses different numerical approaches to optimizing trajectories, including the gradient method, the second variation method, and a generalized Newton-Raphson method. The paper cites the advantages and disadvantages of each method, and compares the second variation method (a direct method) with the generalized Newton-Raphson method (an indirect method). An example problem illustrates the application of the three methods in minimizing the transfer time of a low-thrust ion rocket between the orbits of Earth and Mars. Another paper discusses an iterative process for steepest-ascent optimization of orbit transfer trajectories to minimize storage requirements such as in reduced memory space utilized in guidance computers. By eliminating state variable storage and control schedule storage, the investigator can achieve reduced memory requirements. Other papers discuss dynamic programming, invariant imbedding, quasilinearization, Hilbert space, and the computational aspects of a time-optimal control problem. The collection is suitable for computer programmers, engineers, designers of industrial processes, and researchers involved in aviation or control systems technology.

Table of contents

• Front Cover
• Computing Methods in Optimization Problems
• Copyright Page
• Table of Contents
• Preface
• LIST OF CONTRIBUTORS
• CHAPTER 1. VARIATIONAL THEORY AND OPTIMAL CONTROL THEORY
• CHAPTER 2. ON THE COMPUTATION OF THE OPTIMAL TEMPERATURE PROFILE IN A TUBULAR REACTION VESSEL
• CHAPTER 3. SEVERAL TRAJECTORY OPTIMIZATION TECHNIQUES
• CHAPTER 4. SEVERAL TRAJECTORY OPTIMIZATION TECHNIQUES
• CHAPTER 5. A STEEPEST-ASCENT TRAJECTORY OPTIMIZATION METHOD WHICH REDUCES MEMORY REQUIREMENTS
• CHAPTER 6. DYNAMIC PROGRAMMING, INVARIANT IMBEDDING AND QUASILINEARIZATION: COMPARISONS AND INTERCONNECTIONS
• CHAPTER 7. A COMPARISON BETWEEN SOME METHODS FOR COMPUTING OPTIMUM PATHS IN THE PROBLEM OF BOLZA
• CHAPTER 8. MINIMIZING FUNCTIONALS ON HILBERT SPACE
• CHAPTER 9. COMPUTATIONAL ASPECTS OF THE TIME-OPTIMAL CONTROL PROBLEM
• CHAPTER 10. AN ON-LINE IDENTIFICATION SCHEME for MULTIVARIABLE NONLINEAR SYSTEMS
• CHAPTER 11. METHOD OF CONVEX ASCENT
• CHAPTER 12. STUDY OF AN ALGORITHM FOR DYNAMIC OPTIMIZATION
• CHAPTER 13. THE APPLICATION OF HYBRID COMPUTERS TO THE ITERATIVE SOLUTION OF OPTIMAL CONTROL PROBLEMS
• CHAPTER 14. SYNTHESIS OF OPTIMAL CONTROLLERS USING HYBRID ANALOG-DIGITAL COMPUTERS
• CHAPTER 15. GRADIENT METHODS FOR THE OPTIMIZATION OF DYNAMIC SYSTEM PARAMETERS BY HYBRID COMPUTATION