ANZIAM J.
46 (2004), 45-66
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An affine scaling interior point backtracking algorithm for nonlinear constrained optimisation
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Detong Zhu
Department of Mathematics
Shanghai Normal University
Shanghai 200234
China
dtzhu@shtu.edu.cn
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Abstract
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In this paper we propose a new affine scaling
interior trust region algorithm with a
nonmonotonic backtracking technique for nonlinear
equality constrained optimisation with
nonnegative constraints on the variables. In
order to deal with large problems, the general
full trust region subproblem is decomposed into a
pair of trust region subproblems in horizontal
and vertical subspaces. The horizontal trust
region subproblem in the algorithm is defined by
minimising a quadratic function subject only to
an ellipsoidal constraint in a null tangential
subspace and the vertical trust region subproblem
is defined by the least squares subproblem
subject only to an ellipsoidal constraint. By
adopting Fletcher's penalty function as the
merit function, combining a trust region strategy
and a nonmonotone line search, the mixing
technique will switch to a backtracking step
generated by the two trust region subproblems to
obtain an acceptable step. The global convergence
of the proposed algorithm is proved while
maintaining a fast local superlinear convergence
rate, which is established under some reasonable
conditions. A nonmonotonic criterion is used to
speed up the convergence progress in some highly
nonlinear cases.
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