A new sequential systems of linear equations algorithm of feasible descent for inequality constrained optimization |
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Authors: | Jin Bao Jian Dao Lan Han Qing Juan Xu |
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Institution: | 1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, P. R. China 2. College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, 530006, P. R. China 3. College of Electrical Engineering, Guangxi University, Nanning, 530004, P. R. China 4. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China 5. College of Mathematical Science, Guangxi Teachers Education University, Nanning, 530001, P. R. China
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Abstract: | Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems
of linear equations (SSLE) algorithm generating feasible iterates is proposed for solving nonlinear optimization problems
with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations,
which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible
descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the
global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations
with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly
convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that
an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary
implementation has been tested. |
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Keywords: | Inequality constraints nonlinear optimization systems of linear equations global conver-gence superlinear convergence |
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