  The definition of factor space and a unified optimization based
classification model were developed for linear programming. Intelligent
behaviour appeared in a decision process can be treated as a point y, the
dynamic state observed and controlled by the agent, moving in a factor space
impelled by the goal factor and blocked by the constraint factors. Suppose that
the feasible region is cut by a group of hyperplanes, when point y reaches the
region's wall, a hyperplane will block the moving and the agent needs to adjust
the moving direction such that the target is pursued as faithful as possible.
Since the wall is not able to be represented to a differentiable function, the
gradient method cannot be applied to describe the adjusting process. We,
therefore, suggest a new model, named linear adjusting programming (LAP) in
this paper. LAP is similar as a kind of relaxed linear programming (LP), and
the difference between LP and LAP is: the former aims to find out the ultimate
optimal point, while the latter just does a direct action in short period. You
may ask: Where will a blocker encounter? How can the moving direction be
adjusted? Where further blockers may be encountered next, and how should the
direction be adjusted again? We request at least an adjusting should be
achieved at the first time. If a hyperplane blocks y going ahead along with the
direction d, then we must adjust the new direction d' as the projection of g in
the blocking plane. If there is only one blocker at a time, it is
straightforward to calculate the projection, but how to calculate the
projection when there are more than one blocker encountered simultaneously? We
suggest a projection calculation by means of the Hat matrix in this paper.
Linear adjusting programming will attract interest in many fields. It might
bring a new light to solve the linear programming problem with a strong
polynomial solution.
