Structure Exploitation in an Interior-Point Method for Fully Discretized, State Constrained Optimal Control Problems

作     者：Huber, Andreas Gerdts, Matthias Bertolazzi, Enrico 

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.