An interior trust region algorithm for solving linearly constrained nonlinear optimization |
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Authors: | Ou Yigui Hou Dingpi |
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Affiliation: | 1. Department of Applied Mathematics, Hainan University, 570228, Haikou, Hainan, P. R. China 2. Department of Mathematics, USTC, 230026, Hefei, Anhui, P.R. China
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Abstract: | In this paper, an interior point algorithm based on trust region techniques is proposed for solving nonlinear optimization problems with linear equality constraints and nonnegative variables. Unlike those existing interior-point trust region methods, this proposed method does not require that a general quadratic subproblem with a trust region bound be solved at each iteration. Instead, a system of linear equations is solved to get a search direction, and then a linesearch of Armijo type is performed in this direction to obtain a new iteration point. From a computational point of view, this approach may in general reduce a computational effort, and thus improve the computational efficiency. Under suitable conditions, it is proven that any accumulation of the sequence generated by the algorithm satisfies the first-order optimality condition. |
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