Optimality

The optimal estimate is defined as the one in that minimizes the instability

Obviously, is positive for all and hence the minimal solution always exists. The minimal solution tends to increase values in the global sense and thus maximizes the extent to which an exemplary configuration remains to be the global energy minimum when the observation d is perturbed. It is also expected that with such a , local minima corresponding to some low energy-valued f are least likely to occur in minimization.

The correctness in (7.7), instability in (7.11) and optimality in (7.16) are defined without specifying the form of the energy . Therefore, the principle established so far is general for any optimization-based recognition models. Minimizing the instability with the constraint of the correctness is a nonlinear programming problem when the instability is nonlinear in .

For conciseness, in the following, the superscript will be omitted most of the time unless when necessary.