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mathematics
Conjugate gradient
I often hear people reference the conjugate gradient algorithm as though it can be used as a general algorithm for minimizing any continuous function, though one may have to assume that it is Lipschitz or convex.
When I try to understand conjugate gradient (e.g., the "without agonizing pain" tutorial), it sounds like conjugate gradient is meant for problems only of the form
Ax=b
where A is a matrix and x and b are vectors (x unknown, solving for x).
How can I use conjugate gradient to solve a problem of the form: find an x that is a local minimum for f(x)? Is there a conversion between these two problem types that I'm missing? Can conjugate gradient be used in this way?
When I try to understand conjugate gradient (e.g., the "without agonizing pain" tutorial), it sounds like conjugate gradient is meant for problems only of the form
Ax=b
where A is a matrix and x and b are vectors (x unknown, solving for x).
How can I use conjugate gradient to solve a problem of the form: find an x that is a local minimum for f(x)? Is there a conversion between these two problem types that I'm missing? Can conjugate gradient be used in this way?