关键词: 不等式约束最小二乘, 有效集方法, 反正切变换, 正弦变换, 非线性最小二乘

Abstract: When the constraints in least squares adjustment model are bounded,it is solved by constrained optimization theory.The searching direction is necessarily feasible and descendent.While in unconstrained optimization problem,it is not necessary to consider the feasibility of the searching direction.Thus unconstrained optimization is simpler than the corresponding constrained one.In this paper,the model parameters with bounded constraints are transformed with two typical variables substitution and the constrained least squares problem is thus converted to an unconstrained nonlinear least squares problem.The examples demonstrate that this method is feasible and effective.

Key words: inequality constrained least squares, active set method, arc tangent transformation, sine transformation, nonlinear least squares