  Assume that f is a strict convex function with a unique minimum in R^n. We
divide the vector of n-variables to d groups of vector subvariables with d at
least two. We assume that we can find the partial minimum of f with respect to
each vector subvariable while other variables are fixed. We then describe an
algorithm that partially minimizes each time on a specifically chosen vector
subvariable. This algorithm converges geometrically to the unique minimum. The
rate of convergence depends on the uniform bounds on the eigenvalues of the
Hessian of f in the compact sublevel set f whose values are at most f(x_0),
where x_0 is the starting point of the algorithm. In the case where f is a
polynomial of degree two, with positive definite quadratic term, and d=n our
method can be considered as a generalization of the classical conjugate
gradient method. The main result of this paper is the observation that the
celebrated Sinkhorn diagonal scaling algorithm for matrices, and the
corresponding diagonal scaling of tensors, can be viewed as partial
minimization of certain logconvex functions.
