A Fast Search Algorithm in Adjustment Model with Inequality Constraint

There usually exists some prior information with inequality constraint in the survey of adjustment model. The uniqueness and stability of the solution can be guaranteed by making full use of it. However, the existing adjustment algorithms with inequality constrain, which are mainly based on optimization theory, are usually complex. They need to select the effective constraint or establish penalty function. This paper mainly studies the adjustment model with inequality constraint, in which the inequality constraint is considered as a feasible region on the basis of the least squares adjustment rule and the Fisher function is used to search the optimal solution that minimizes the sum of squared errors, and sufficient necessary conditions for the optimal feasible solution are derived. A non-precise fast search based on Wolfe-Powell algorithm is given in the feasible region, which reduces the computational complexity, a new adjustment algorithm with inequality constraint is presented. The given algorithm, in which the adjustment criterion is consistent with that of the least squares adjustment criteria, does not require matrix inversion operation, and can solve some of the large dimension adjustment problem with inequality constrain.