We are interested in building low-dimensional surrogate models to reduce optimization costs, while having theoretical guarantees that the optimum will satisfy the constraints of the full-size model, by making conservative approximations. The surrogate model is constructed using a Gaussian process regression (GPR). To ensure conservativeness, two new approaches are proposed: the first one using bootstrapping, and the second one using concentration inequalities. Those two techniques are based on a stochastic argument and thus will only enforce conservativeness up to a user-defined probability threshold. The method has applications in the context of optimization using the active subspace method for dimensionality reduction of the objective function and the constraints, addressing recorded issues about constraint violations. The resulting algorithms are tested on a toy optimization problem in thermal design.

翻译：我们旨在构建低维代理模型以降低优化成本，同时通过保守近似保证最优解满足全尺寸模型的约束条件。该代理模型采用高斯过程回归构建。为确保保守性，本文提出两种新方法：第一种基于自助法，第二种利用浓度不等式。这两种技术均基于随机性论证，因此仅能在用户定义的概率阈值内保证保守性。该方法可应用于采用主动子空间方法对目标函数和约束进行降维的优化场景，解决已有研究中关于约束违反的记录问题。最终算法在热设计领域的基准优化问题上进行了测试。