Interior-Point Polynomial Algorithms in Convex Programming

By Yurii Nesterov & Arkadi Nemirovskii, ISBN 0-89871-319-6
Written for users interested in optimization, this text presents the generaltheory of interior-point polynomial-time methods for convex programming.The authors try to demonstrate that all known polynomial-time interior-pointmethods can be explained on a general theory basis, and hence extendedinto a wide variety of nonlinear convex problems. This is shown by developingnew polynomial time interior-point methods for many important classesof problems. The theory presented in the text, including applicationsin control system design, are implemented in the LMI Control Toolbox developedby Pascal Gahinet, Arkadi Nemirovskii, Alan J. Laub, and Mahmoud Chilali.The toolbox may be purchased from The MathWorks.