论文标题
基于模型的无导数优化方法和软件
Model-Based Derivative-Free Optimization Methods and Software
论文作者
论文摘要
本文研究无衍生化的优化（DFO），尤其是基于模型的方法和软件。这些方法是由优化问题激励的，这些优化问题是访问目标函数以及可能的约束功能的一阶信息是不可能或过高的。 特别是，本文提出了PDFO，我们开发了一个软件包，以提供MATLAB和PYTHON接口到Powell基于模型的DFO求解器，即Cobyla，Uobyqa，Newuoa，Bobyqa和Lincoa。此外，本文的重要部分致力于基于顺序二次编程（SQP）方法开发一种新的DFO方法。因此，我们介绍了SQP方法的概述，并就其理论和实践提供了一些观点。特别是，我们表明SQP子问题的目标函数是表面切线空间中原始目标函数的自然二次近似。最后，我们详细介绍了开发新的DFO方法，该方法在通过二次近似限制的约束优化后，称为CobyQA。这种无衍生的信任区域SQP方法旨在解决接受平等和不平等约束的非线性约束优化问题。 CobyQA的一个重要特征是，它始终尊重约束约束（如果有），这是由目标函数在违反界限时未定义的应用所激发的。我们揭示了CobyQA的广泛数值实验，与Powell的DFO求解器相比，CobyQA的优势明显。这些实验表明，CobyQA是Cobyla作为通用DFO求解器的出色继任者。 这是博士学位。论文在香港理工大学的Zaikun Zhang博士和小陈教授的监督下完成。香港的教资会在香港博士学位上提供了财政支持。奖学金计划。
This thesis studies derivative-free optimization (DFO), particularly model-based methods and software. These methods are motivated by optimization problems for which it is impossible or prohibitively expensive to access the first-order information of the objective function and possibly the constraint functions. In particular, this thesis presents PDFO, a package we develop to provide both MATLAB and Python interfaces to Powell's model-based DFO solvers, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. Moreover, a significant part of this thesis is devoted to developing a new DFO method based on the sequential quadratic programming (SQP) method. Therefore, we present an overview of the SQP method and provide some perspectives on its theory and practice. In particular, we show that the objective function of the SQP subproblem is a natural quadratic approximation of the original objective function in the tangent space of a surface. Finally, we elaborate on developing our new DFO method, named COBYQA after Constrained Optimization BY Quadratic Approximations. This derivative-free trust-region SQP method is designed to tackle nonlinearly constrained optimization problems that admit equality and inequality constraints. An important feature of COBYQA is that it always respects bound constraints, if any, which is motivated by applications where the objective function is undefined when bounds are violated. We expose extensive numerical experiments of COBYQA, showing evident advantages of COBYQA compared with Powell's DFO solvers. These experiments demonstrate that COBYQA is an excellent successor to COBYLA as a general-purpose DFO solver. This is the Ph.D. thesis finished under the supervision of Dr. Zaikun Zhang and Prof. Xiaojun Chen at The Hong Kong Polytechnic University. Financial support was provided by the UGC of Hong Kong under the Hong Kong Ph.D. Fellowship Scheme.
