Minimum-Volume Ellipsoids
Theory and Algorithms
MPS-SIAM Series on Optimization Series

The first book in the area, this volume addresses the problem of finding an ellipsoid to represent a large set of points in high-dimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. While algorithms of this kind have been discovered and rediscovered over the past fifty years, their computational complexities and convergence rates have only recently been investigated. The optimization problems in the book have the entries of a symmetric matrix as their variables, so the author's treatment also gives an introduction to recent work in matrix optimization. This book will be of interest to graduate students and researchers in operations research, theoretical statistics, data mining, complexity theory, computational geometry, and computational science.

List of figures; List of algorithms; Preface; 1. Introduction; 2. Minimum-volume ellipsoids; 3. Algorithms for the MVEE problem; 4. Minimum-area ellipsoidal cylinders; 5. Algorithms for the MAEC problem; 6. Related problems and algorithms; Appendix A. Background material; Appendix B. MATLAB codes; Bibliography; Index.

Michael J. Todd is Leon C. Welch Professor Emeritus of the School of Operations Research and Information Engineering at Cornell University. He received a Guggenheim Fellowship (1980–1981), a Sloan Research Fellowship (1981–1985), the George B. Dantzig Prize (1988) and the John von Neumann Theory Prize (2003). He is an INFORMS Fellow and a SIAM Fellow. He has served on the editorial boards of Mathematics of Operations Research, Operations Research, and the SIAM Journal on Optimization. He was also Managing Editor of Foundations of Computational Mathematics and has served on the boards of Acta Numerica and Foundations and Trends in Optimization. He is the author of one book and the co-editor of five others.