Kruk, Serge.2006-07-282006-07-2820012001http://hdl.handle.net/10012/629We present a new family of search directions and of corresponding algorithms to solve conic linear programs. The implementation is specialized to semidefinite programs but the algorithms described handle both nonnegative orthant and Lorentz cone problems and Cartesian products of these sets. The primary objective is not to develop yet another interior-point algorithm with polynomial time complexity. The aim is practical and addresses an often neglected aspect of the current research in the area, accuracy. Secondary goals, tempered by the first, are numerical efficiency and proper handling of sparsity. The main search direction, called Gauss-Newton, is obtained as a least-squares solution to the optimality condition of the log-barrier problem. This motivation ensures that the direction is well-defined everywhere and that the underlying Jacobian is well-conditioned under standard assumptions. Moreover, it is invariant under affine transformation of the space and under orthogonal transformation of the constraining cone. The Gauss-Newton direction, both in the special cases of linear programming and on the central path of semidefinite programs, coincides with the search directions used in practical implementations. Finally, the Monteiro-Zhang family of search directions can be derived as scaled projections of the Gauss-Newton direction.application/pdf5822496 bytesapplication/pdfenCopyright: 2001, Kruk, Serge.. All rights reserved.Harvested from Collections CanadaDoctoral Thesis