<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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 formulate 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.</p></abstract>

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 formulate 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.

Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point Methods

Institute of Control and Computation Engineering Faculty of Electronics and Information Technology, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland

Research and Academic, Computer Network (NASK), ul. Wąwozowa 18, 02-796 Warsaw, Poland

International Journal of Applied Mathematics and Computer Science

The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic...

Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point Methods

Publié en ligne: 07 janv. 2008

Pages: 515 - 537

DOI: https://doi.org/10.2478/v10006-007-0043-y

Mots clés
dynamic optimization, large-scale optimization, sequential quadratic programming, nonlinear interior-point methods, object-oriented numerical computations, automatic differentiation, performance data analysis

This content is open access.

Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point Methods

Publié en ligne: 07 janv. 2008

Pages: 515 - 537

DOI: https://doi.org/10.2478/v10006-007-0043-y

Mots clésdynamic optimization, large-scale optimization, sequential quadratic programming, nonlinear interior-point methods, object-oriented numerical computations, automatic differentiation, performance data analysis

This content is open access.

Mots clés
dynamic optimization, large-scale optimization, sequential quadratic programming, nonlinear interior-point methods, object-oriented numerical computations, automatic differentiation, performance data analysis