A new affine scaling interior point algorithm for nonlinear optimization subject to linear equality and inequality constraints

Authors:
Detong Zhu
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 6
Cited 0

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Abstract

In this paper we propose a new interior affine scaling region algorithm with nonmonotonic interior point backtracking technique for nonlinear optimization subject to linear equality and inequality constraints. The trust region subproblem in the proposed algorithm is defined by minimizing a quadratic function subject only to an affine scaling ellipsoidal constraint in a null subspace of the extended equality constraints. Using both trust region strategy and line search technique, the affine scaling trust region subproblem at each iteration generates backtracking interior step to obtain a new accepted step. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases.