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Linear Optimization (LO) is one of the most widely taught and fast developing techniques in mathematics, with applications in many areas of science, commerce and industry. The dramatically increased interest in the subject is due mainly to advances in computer technology and to the development of Interior Point Methods (IPM) for LO. This book provides a unified presentation of the field by way of an interior point approach to both the theory of LO and algorithms for LO (design, convergence, complexity and asymptotic behaviour). A common thread throughout the book is the role of strictly complementary solutions, which play a crucial role in the interior point approach and distinguishes the new approach from the classical Simplex-based approach.