Exploring novel designs of NLP solvers: Architecture and Implementation of WORHP

Mathematical Optimization in general and Nonlinear Programming in particular, are applied by many scientific disciplines, such as the automotive sector, the aerospace industry, or the space agencies. With some established NLP solvers having been available for decades, and with the mathematical community being rather conservative in this respect, many of their programming standards are severely outdated. It is safe to assume that such usability shortcomings impede the wider use of NLP methods; a representative example is the use of static workspaces by legacy FORTRAN codes. This dissertation gives an account of the construction of the European NLP solver WORHP by using and combining software standards and techniques that have not previously been applied to mathematical software to this extent. Examples include automatic code generation, a consistent reverse communication architecture and the elimination of static workspaces. The result is a novel, industrial-grade NLP solver that overcomes many technical weaknesses of established NLP solvers and other mathematical software

High performance implementation of MPC schemes for fast systems

In recent years, the number of applications of model predictive control (MPC) is rapidly increasing due to the better control performance that it provides in comparison to traditional control methods. However, the main limitation of MPC is the computational e ort required for the online solution of an optimization problem. This shortcoming restricts the use of MPC for real-time control of dynamic systems with high sampling rates. This thesis aims to overcome this limitation by implementing high-performance MPC solvers for real-time control of fast systems. Hence, one of the objectives of this work is to take the advantage of the particular mathematical structures that MPC schemes exhibit and use parallel computing to improve the computational e ciency. Firstly, this thesis focuses on implementing e cient parallel solvers for linear MPC (LMPC) problems, which are described by block-structured quadratic programming (QP) problems. Speci cally, three parallel solvers are implemented: a primal-dual interior-point method with Schur-complement decomposition, a quasi-Newton method for solving the dual problem, and the operator splitting method based on the alternating direction method of multipliers (ADMM). The implementation of all these solvers is based on C++. The software package Eigen is used to implement the linear algebra operations. The Open Message Passing Interface (Open MPI) library is used for the communication between processors. Four case-studies are presented to demonstrate the potential of the implementation. Hence, the implemented solvers have shown high performance for tackling large-scale LMPC problems by providing the solutions in computation times below milliseconds. Secondly, the thesis addresses the solution of nonlinear MPC (NMPC) problems, which are described by general optimal control problems (OCPs). More precisely, implementations are done for the combined multiple-shooting and collocation (CMSC) method using a parallelization scheme. The CMSC method transforms the OCP into a nonlinear optimization problem (NLP) and de nes a set of underlying sub-problems for computing the sensitivities and discretized state values within the NLP solver. These underlying sub-problems are decoupled on the variables and thus, are solved in parallel. For the implementation, the software package IPOPT is used to solve the resulting NLP problems. The parallel solution of the sub-problems is performed based on MPI and Eigen. The computational performance of the parallel CMSC solver is tested using case studies for both OCPs and NMPC showing very promising results. Finally, applications to autonomous navigation for the SUMMIT robot are presented. Specially, reference tracking and obstacle avoidance problems are addressed using an NMPC approach. Both simulation and experimental results are presented and compared to a previous work on the SUMMIT, showing a much better computational e ciency and control performance.Tesi

PARALLEL ALGORITHMS FOR NONLINEAR PROGRAMMING AND APPLICATIONS IN PHARMACEUTICAL MANUFACTURING

Effective manufacturing of pharmaceuticals presents a number of challenging optimization problems due to complex distributed, time-independent models and the need to handle uncertainty. These challenges are multiplied when real-time solutions are required. The demand for fast solution of nonlinear optimization problems, coupled with the emergence of new concurrent computing architectures, drives the need for parallel algorithms to solve challenging NLP problems. The goal of this work is the development of parallel algorithms for nonlinear programming problems on different computing architectures, and the application of large-scale nonlinear programming on challenging problems in pharmaceutical manufacturing

A generic interior-point framework for nonsmooth and complementarity constrained nonlinear optimization

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