Mathematical Optimization Techniques

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND. Richard Bell Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii PART ONE: AIRCRAFT, ROCKETS, AND GUIDANCE 1. A Survey of the Problem of Optimizing Flight Paths of Aircraft and Missiles, by Angelo Miele. . . . ...... .. ... .. 3 2. Estimating Performance Capabilities of Boost Rockets, by P. Dergarabedian and R. P. Ten Dyke. .. . .. ... . .. .. . 33 3. The Optimum Spacing of Corrective Thrusts in Interplanetary Navigation, by J. V. Breakwell... . . . . . . . . . . . . 59 4. The Analysis and Solution of Optimum Trajectory Problems, by Stuart E. Dreyfus. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 PART TWO: COMMUNICATION, PREDICTION, AND DECISION 5. A New Approach to the Synthesis of Optimal Smoothing and Prediction Systems, by Emanuel Parzen. . . . . . . . . . . . 75 6. Adaptive Matched Filters, by Thomas Kailath. . . . . . . . .. 109 7. Optimization Problems in Statistical Communication Theory, by David Middleton . .................... '" .. 141 8. Estimators with Minimum Bias, by William Jackson Hall. . 167 9. On Optimal Replacement Rules When Changes of State Are Markovian, by C. Derman. . .. . . ... .. .. . . .. .. . . . .. 201 PART THREE: PROGRAMMING, COMBINATORICS, AND DESIGN 10. Simplex Method and Theory, by A. W. Tucker.... ...... 213 11. The Present Status of Nonlinear Programming, by P . Wolfe 233 vi Contents 12. The Number of Simplices in a Complex, by Joseph B. Kruskal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 251 13. Optimization in Structural Design, by William Prager.... 279 14. Geometric and Game-Theoretic Methods in Experimental Design, by G. Elfving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 291 PART FOUR: MODELS, AUTOMATION, AND CONTROL 15. Automation and Control in the Soviet Union, by J. P. LaSalle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 303 16. The Theory of Optimal Control and the Calculus of Variations, by R. E. Kalman . ............ " ....... , .. .. ... 309 17. Mathematical Model Making as an Adaptive Process, by Richard Bellman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 333 Index........................................... " ..... , 341