A redesign of Interior Point Methods (IPMs) for LP/QP problems will be addressed. Its objective is to avoid an explicit access to the problem data and to allow only matrix-vector products to be executed with the Hessian and Jacobian and its transpose. A use of iterative methods and a choice of suitable preconditioner to solve reduced Newton systems arising in optimization with IPMs will be discussed. A new fast preconditioner will be presented. Its numerical properties will be analysed and its use will be illustrated by computational results obtained for a collection of small to medium scale optimization problems (with no more than one million variables and with matrices limited to at most 10 million of nonzero elements).
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