Computational Issues in High Performance Software for by Almerico Murli, Gerardo Toraldo

By Almerico Murli, Gerardo Toraldo

A distinct factor of , v.7, no.1 (1997), containing papers from a June 1995 convention held in Capri, Italy. Papers evaluate fresh advancements relating to software program for nonlinear optimization, reflecting assorted views on well-established algorithms for nonlinear difficulties, quick algorithms for large-scale optimization difficulties, direct tools for answer of sparse linear algebra difficulties, and LCP solvers.

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This strategy must be used with care. We should not use the sparse AD option to obtain the sparsity pattern at the starting point because the starting point is invariably special, and not representative of a general point in the region V of interest. In particular, there are usually many symmetries in the starting point that are not necessarily present in intermediate iterates. We can also use the sparse AD option for a number of iterates until we feel that any symmetries present in the starting point have been removed by the optimization algorithm.

9] and is based upon incorporating the equality constraints via a Lagrangian barrier function whilst handling upper and lower bounds directly. The sequential, approximate minimization of the Lagrangian barrier function is performed in a trust region framework such as that proposed by Conn et al. [5]. Our aim in this paper is to consider how these two different algorithms mesh together. In particular, we aim to show that ultimately very little work is performed in the iterative sequential minimization algorithm for every iteration of the outer Lagrangian barrier algorithm.

An important design goal of ELSO is to avoid this requirement. S. Department of Energy, under Contract W-3 1-109-Eng38, and by the National Science Foundation, through the Center for Research on Parallel Computation, under Cooperative Agreement No. CCR-9 120008. 28 BOUARICHA AND M O R E where hi is the difference parameter, and ei is the i-th unit vector, but this approximation suffers from truncation errors, which can cause premature termination of an optimization algorithm far away from a solution.

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