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Object-oriented approaches to large-scale nonlinear programming for process systems engineering.

机译：面向对象的方法，用于过程系统工程的大规模非线性编程。

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This thesis concerns the numerical solution of large-scale NonLinear Programs (NLPs) for process systems engineering and other types of related optimization problems. Described here is a new approach for modeling and implementating reduced space Successive Quadratic Programming (rSQP) algorithms. An object-oriented methodology is used to develop a framework for rSQP called rSQP++ in C++. The goals for rSQP++ are quite lofty. The rSQP++ framework is being designed to incorporate many different SQP algorithms and to allow external configuration of specialized linear algebra objects such as vectors, matrices and linear solvers. In addition, it is possible for the client to modify the SQP algorithms to meet other specialized needs without having to touch any of the source code within the rSQP++ framework.; Another aspect to this thesis is devoted to finding ways to extend rSQP to NLPs with more degrees of freedom. In this vein, a new dual space, active set, Schur complement Quadratic Programming (QP) solver called QPSchur is described. Not only has QPSchur been shown to be more computationally efficient than several other QP solvers on many problems, but its ability to be externally configured with specialized linear algebra options is also demonstrated. Also, strategies for reducing the cost of quasi-Newton Hessian approximations are investigated for use in rSQP. A compact limited memory BFGS approximation has been implemented and explored and a projected BFGS approach in the space of the superbasic variables has been investigated. Numerical results demonstrate the dramatic impact these two measures can have in reducing the computation time.; This work is demonstrated on several different NLPs from various application areas. The effectiveness of using QPSchur as the QP solver in a Model Predictive Control (MPC) application for a specialized paper process is proven. This new MPC controller is shown to be two orders of magnitude faster than a currently used MPC controller in Matlab. Nonlinear MPC (NMPC) is also considered. The example process is the difficult Tennessee Eastman challenge problem. Here rSQP++ is compared to an interior-point solver IPOPT. Some of the tradeoffs between active set and interior point NLP solvers for use with NMPC are demonstrated on this difficult problem.; Finally, the use of rSQP for PDE constrained optimization is explored, along with its extension to distributed memory, parallel computing environments. Here, a “Tailored Approach” interface and a PDE simulation code MPSalsa is developed and used to solve a Chemical Vapor Decomposition (CVD) design problem in an order of magnitude less time than a currently used “Black Box” approach. Open questions for PDE constrained optimization are discussed and the difficulties in allowing the parallelization of rSQP++ are described. To address the difficulties in allowing optimization codes to exploit special computing environments without be taken over, a new and novel object-oriented design for vectors and vector reduction/transformation operators is described in great detail. Adopting such a design will allow the basic linear algebra operations used in an optimization code to be taken over by a specialized application without having to touch or even recompile one line of core code in the optimization algorithm.
机译：本文涉及用于过程系统工程和其他类型的相关优化问题的大型非线性程序（NLP）的数值解。这里介绍了一种用于建模和实现缩减空间的连续二次编程（rSQP）算法的新方法。面向对象的方法用于开发C ++中称为rSQP ++的rSQP框架。 rSQP ++的目标很高。 rSQP ++框架旨在集成许多不同的SQP算法，并允许对专用线性代数对象（例如向量，矩阵和线性求解器）进行外部配置。另外，客户可以修改SQP算法以满足其他特殊需求，而无需接触rSQP ++框架内的任何源代码。本论文的另一个方面致力于寻找将rSQP扩展到具有更大自由度的NLP的方法。在这种情况下，描述了一种称为QPSchur的新的双重空间有效集Schur补码二次规划（QP）求解器。在许多问题上，不仅证明QPSchur在计算上比其他几个QP解算器更有效，而且还证明了其可以使用专用的线性代数选择进行外部配置。此外，研究了用于rSQP的降低准牛顿黑森近似值成本的策略。一个紧凑的有限内存BFGS逼近已被实现和探索，并研究了超基本变量空间中的BFGS投影方法。数值结果表明，这两种措施对减少计算时间都具有巨大的影响。这项工作在来自不同应用领域的几个不同的NLP上得到了证明。事实证明，在专用纸工艺的模型预测控制（MPC）应用程序中将QPSchur用作QP求解器的有效性。事实证明，这种新的MPC控制器比Matlab中当前使用的MPC控制器快两个数量级。还考虑了非线性MPC（NMPC）。示例过程是田纳西伊士曼难题。在这里，将rSQP ++与内点求解器IPOPT进行比较。关于这个难题，论证了与NMPC一起使用的有源集和内点NLP求解器之间的一些权衡。最后，探索了将rSQP用于PDE约束优化，以及将其扩展到分布式内存，并行计算环境。在这里，开发了“量身定制的方法”界面和PDE仿真代码MPSalsa，并用于解决化学气相分解（CVD）设计问题，所需时间比当前使用的“黑匣子”方法少了一个数量级。讨论了有关PDE约束优化的未解决问题，并描述了允许rSQP ++并行化的困难。为了解决允许优化代码在不接管的情况下利用特殊计算环境的难题，将对矢量和矢量归约/变换运算符的新颖新颖的面向对象设计进行详细描述。采用这样的设计将使优化代码中使用的基本线性代数运算由专门的应用程序接管，而不必触摸甚至重新编译优化算法中的一行核心代码。

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