Justin Chang <[email protected]> writes: > Hi Jason, > > One more question about BLMVM... if it only uses gradient information and > does not require the definitition of a Hessian Matrix, can this method be > applied to solve problems that are nonsymmetric by nature? (e.g., > advection-diffusion equations).
Such equations do not have an associated objective functional, thus you don't have the "gradient" of something, you just have a system of nonlinear equations. (There are ways to formulate such systems as optimization, but they have issues like you mention.) Reformulating nonlinear equations as optimization can also turn a problem with a unique solution into one with local minima, for which it may be impossible to guarantee that you have reached a global minimum. Use SNES for solving nonlinear equations. You can try the quasi-Newton methods, which are related to BLMVM.
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