首页> 外文期刊>International Journal of Applied Mathematics and Computer Science >OBJECT LIBRARY OF ALGORITHMS FOR DYNAMIC OPTIMIZATION PROBLEMS: BENCHMARKING SQP AND NONLINEAR INTERIOR POINT METHODS
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OBJECT LIBRARY OF ALGORITHMS FOR DYNAMIC OPTIMIZATION PROBLEMS: BENCHMARKING SQP AND NONLINEAR INTERIOR POINT METHODS

机译:动态优化问题的算法目标库:Benchmarking SQP和非线性内部点方法

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The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we briefly formulaic and characterize the class of problems solved by our optimization classes. The solution of dynamic optimization problems with general constraints is performed by transformation into structured large-scale nonlinear programming problems and applying methods for nonlinear optimization. Two main algorithms of solvers for constrained dynamic optimization are presented in detail: the sequential quadratic programming (SQP) exploring the multistage structure of the dynamic optimization problem during the solution of a sequence of quadratic subproblems, and the nonlinear interior-point method implemented in a general-purpose large-scale optimizer IPOPT. At the end, we include a typical numerical example of the application of the constrained solvers to a large-scale discrete-time optimal control problem and we use the performance profiles methodology to compare the efficiency and robustness of different solvers or different options of the same solver. In conclusions, we summarize our experience gathered during the library development.
机译:本文的主要目的是描述动态优化问题的面向对象算法库的设计,实现和可能性。我们简要介绍了用于动态优化问题的表述和处理的库类,并对无约束和约束优化的求解器类进行了概述。我们还演示了我们使用的导数评估方法,尤其是自动微分。此外,我们简要地阐述并描述了由优化类解决的问题的类。具有一般约束的动态优化问题的解决方案是通过转换为结构化的大规模非线性规划问题并应用非线性优化方法来进行的。详细介绍了用于约束动态优化的求解器的两种主要算法:顺序二次编程(SQP),用于在解决一系列二次子问题的过程中探索动态优化问题的多级结构,以及在一个子程序中实现的非线性内点方法。通用大型优化器IPOPT。最后,我们提供了一个典型的数值示例,说明了约束求解器在大规模离散时间最优控制问题中的应用,并且我们使用性能曲线方法来比较不同求解器或相同求解器的不同选项的效率和鲁棒性解算器。最后,我们总结了在图书馆开发过程中积累的经验。

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