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作者机构:Bundeswehr Univ Munich Werner Heisenberg Weg 39 D-85577 Neubiberg Germany Univ Trento Via Sommar 9 I-38123 Trento Italy
出 版 物:《VIETNAM JOURNAL OF MATHEMATICS》 (越南数学杂志)
年 卷 期:2018年第46卷第4期
页 面:1089-1113页
学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题:Optimal control Direct discretization method Interior-point method Structure exploitation
摘 要:We discuss a direct discretization method for state-constrained optimal control problems and an interior-point method, which is used to solve the resulting large-scale and sparse nonlinear optimization problems. The main focus of the paper is on the investigation of an efficient method to solve the occurring linear equations with saddle-point structure. To this end, we exploit the particular structure that arises from the optimal control problem and the discretization scheme and use a tailored linear algebra solver ALGLIN in combination with a re-ordering of the saddle-point matrices. Numerical experiments for a simple optimal control problem show a significant speed-up compared to state-of-the-art sparse LU decomposition methods like MA57 or MUMPS in combination with IPOPT.