论文标题
无衍生的无限限制优化，用于用替代模型解决结构化问题
Derivative-Free Bound-Constrained Optimization for Solving Structured Problems with Surrogate Models
论文作者
论文摘要
我们提出和分析一种基于模型的无衍生物（DFO）算法，用于求解目标函数是光滑函数的组成和黑框函数的向量。我们假设黑框函数是光滑的，并且评估是算法的计算瓶颈。我们算法的区别特征是在插值点上使用近似函数值，可以通过廉价评估的应用特定的替代模型获得。例如，我们考虑解决一系列相关优化问题并呈现基于回归的近似方案的情况，该方案使用在求解先前的问题实例时评估的函数值。此外，我们提出并分析了一种新算法，用于获取处理不可行的结合约束的插值点。我们的数值结果表明，当有黑盒函数评估的历史记录时，我们的算法优于最新的DFO算法，用于从化学工程应用中解决最小二乘问题。
We propose and analyze a model-based derivative-free (DFO) algorithm for solving bound-constrained optimization problems where the objective function is the composition of a smooth function and a vector of black-box functions. We assume that the black-box functions are smooth and the evaluation of them is the computational bottleneck of the algorithm. The distinguishing feature of our algorithm is the use of approximate function values at interpolation points which can be obtained by an application-specific surrogate model that is cheap to evaluate. As an example, we consider the situation in which a sequence of related optimization problems is solved and present a regression-based approximation scheme that uses function values that were evaluated when solving prior problem instances. In addition, we propose and analyze a new algorithm for obtaining interpolation points that handles unrelaxable bound constraints. Our numerical results show that our algorithm outperforms a state-of-the-art DFO algorithm for solving a least-squares problem from a chemical engineering application when a history of black-box function evaluations is available.
