  A Krein space H and bounded linear operators B, C on H are given. Then, some
min and max problems about the operators (BX - C)^{#}(BX -C), where X runs over
the space of all bounded linear operators on H, are discussed. In each case, a
complete answer to the problem, including solvability conditions and
characterization of the solutions, is presented. Also, an adequate
decomposition of B is considered and the min-max problem is addressed. As a
by-product the Moore-Penrose inverse of B is characterized as the only solution
of a variational problem. Other generalized inverses are described in a similar
fashion as well.
