"Direct Search" Solution of Numerical and Statistical Problems

"Direct Search" Solution of Numerical and Statistical Problems

Received May, 1960; revised October, 1960. | ROBERT HOOKE AND T. A. JEEVES
The paper introduces and discusses the "direct search" method for solving numerical and statistical problems, which is particularly useful when classical methods are infeasible. The authors describe the method as a sequential examination of trial solutions, comparing each with the best solution obtained so far and using a strategy to determine the next trial solution. The method is favored for its simplicity and efficiency, especially on electronic computers, and it provides approximate solutions that improve with each step. The paper also highlights the method's ability to handle problems with different assumptions about the functions involved and its potential for solving large systems of equations. The authors provide examples of using direct search in curve fitting, solving integral equations, and maximizing or minimizing functions, demonstrating its effectiveness in cases where classical methods fail. They also introduce pattern search, a specific type of direct search routine, and discuss its advantages in handling ill-conditioned matrices and sharp valleys in function surfaces. The paper concludes by emphasizing the practical importance of direct search techniques and their potential to stimulate new concepts in functional classification.The paper introduces and discusses the "direct search" method for solving numerical and statistical problems, which is particularly useful when classical methods are infeasible. The authors describe the method as a sequential examination of trial solutions, comparing each with the best solution obtained so far and using a strategy to determine the next trial solution. The method is favored for its simplicity and efficiency, especially on electronic computers, and it provides approximate solutions that improve with each step. The paper also highlights the method's ability to handle problems with different assumptions about the functions involved and its potential for solving large systems of equations. The authors provide examples of using direct search in curve fitting, solving integral equations, and maximizing or minimizing functions, demonstrating its effectiveness in cases where classical methods fail. They also introduce pattern search, a specific type of direct search routine, and discuss its advantages in handling ill-conditioned matrices and sharp valleys in function surfaces. The paper concludes by emphasizing the practical importance of direct search techniques and their potential to stimulate new concepts in functional classification.
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