Adjoint based Optimization Methods
by Andreas Griewank
Abstract: As recently confirmed by an NP completeness result of Uwe Naumann the evaluation of Jacobians, Hessians, and other derivative matrices is a potentially costly computational task. In contrast, not only tangents representing Jacobian-vector products but also first and second order adjoints representing vector-Jacobian and Hessian vector products, can be obtained at a cost similar to the underlying vector or scalar function.
After reviewing the above results we discuss their impact on the design of optimization algorithms. I particular we present a new class of adjoint based quasi-Newton updates and a matrix-free one-shot approach to optimizing very large systems like those arising through the discretization of partial differential equations in aerodynamics and geophysics.
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