Grid-based methods for linearly equality constrained optimization problems

This paper describes a direct search method for a class of linearly constrained optimization problem. Through research we find it can be treated as an unconstrained optimization problem. And with the decrease of dimension of the variables need to be computed in the algorithms, the implementation of convergence to KKT points will be simplified to some extent. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.