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Method of Gradients

1962; Elsevier BV; Linguagem: Inglês

10.1016/s0076-5392(08)62094-9

2772-9753

Henry J. Kelley,

Advanced Optimization Algorithms Research

The method of gradients also known as method of steepest descent is an elementary concept for the solution of minimum problems. In recent years the computational appeal of the method has led to its adoption in a variety of application such as —multivariable minimum problems of ordinary calculus, solution of systems of algebraic equations, integral equations, and variational problems. This chapter begins with a discussion of the main features of the gradient method in the context of ordinary minimum problems subject to constraints. It also discusses the variational problems of flight performance, introducing Green's functions in the role played by partial derivatives in ordinary minimum problems and attempting to preserve an analogy between the two classes of problems in the subsequent development. The close relationship between Green's functions or influence functions and the error coefficients of guidance theory has drawn attention to the usefulness of the adjoint system technique in guidance analysis.