The paper "Efficient Global Optimization of Expensive Black-Box Functions" by Donald R. Jones, Matthias Schonlau, and William J. Welch addresses the challenge of optimizing functions with limited evaluations due to time or cost constraints in engineering problems. The authors introduce a response surface methodology that models nonlinear, multimodal functions using stochastic processes, particularly Kriging. This approach helps in visualizing input-output relationships, estimating the optimum, and suggesting points for additional evaluations. The key to this method is balancing the exploitation of the approximating surface with the improvement of the approximation. The paper also discusses the historical context of this methodology in mathematical geology, global optimization, and statistics, highlighting differences in emphasis and application across these fields. The authors aim to develop an efficient global optimization algorithm with a credible stopping rule, overcoming computational challenges that have previously been considered intractable.The paper "Efficient Global Optimization of Expensive Black-Box Functions" by Donald R. Jones, Matthias Schonlau, and William J. Welch addresses the challenge of optimizing functions with limited evaluations due to time or cost constraints in engineering problems. The authors introduce a response surface methodology that models nonlinear, multimodal functions using stochastic processes, particularly Kriging. This approach helps in visualizing input-output relationships, estimating the optimum, and suggesting points for additional evaluations. The key to this method is balancing the exploitation of the approximating surface with the improvement of the approximation. The paper also discusses the historical context of this methodology in mathematical geology, global optimization, and statistics, highlighting differences in emphasis and application across these fields. The authors aim to develop an efficient global optimization algorithm with a credible stopping rule, overcoming computational challenges that have previously been considered intractable.