Newton's Method and Design Optimization
نویسندگان
چکیده
This report discusses design optimizationmethods, many of which are equivalent to classical optimal control methods [1, 2] in the sense that Newton's method is applied to the necessary conditions for optimality. In this context, many design methods are minor variants of the classical Lagrange-Newton method and can be understood by using the theory for Newton's method. In many application areas, variants of Newton's method have been used that have in common an augmented line search that ensures the satisfaction of certain of the nonlinear equations at each Newton iteration. This nonlinear elimination method has recently been analyzed by Lanzkron, Rose, and Wilkes [3] and is of signi cant value in boundary layer coupled CFD [4, 5, 6]. We rst review classical optimal control methods and then show how they can be extended to state equations derived from boundary value problems and to solution-adaptive grid methods. We then derive various proposed decomposition methods in this context and show a relationship between these methods and the inexact nonlinear elimination method. This report owes something to the spirit of [7] in the use of the relationship between methods for solving nonlinear systems of equations and optimization problems.
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