An Aggregate Constraint Method for Inequality-constrained Least Squares Problems |
| |
| Authors: | Junhuan Peng Hongping Zhang Suli Shong Chunxi Guo |
| |
| Institution: | (1) School of Civil Engineering, Chongqing University, Shabei Road 83, Chongqing, 400045, Peoples Republic of China;(2) Shanghai Astronomical Observatory, Chinese Academy of Sciences, Nandan Road 80, Shanghai, 200030, Peoples Republic of China;(3) Geodetic Data Processing Centre, State Bureau of Surveying and Mapping, Youyi dong Road 334, Xian, 710054, Peoples Republic of China;(4) Faculty of Construction, Guangdong University of Technology, Dongfeng Road 729, Guangzhou, Peoples Republic of China |
| |
| Abstract: | The inequality-constrained least squares (ICLS) problem can be solved by the simplex algorithm of quadratic programming. The ICLS problem may also be reformulated as a Bayesian problem and solved by using the Bayesian principle. This paper proposes using the aggregate constraint method of non-linear programming to solve the ICLS problem by converting many inequality constraints into one equality constraint, which is a basic augmented Lagrangean algorithm for deriving the solution to equality-constrained non-linear programming problems. Since the new approach finds the active constraints, we can derive the approximate algorithm-dependent statistical properties of the solution. As a result, some conclusions about the superiority of the estimator can be approximately made. Two simulated examples are given to show how to compute the approximate statistical properties and to show that the reasonable inequality constraints can improve the results of geodetic network with an ill-conditioned normal matrix. |
| |
| Keywords: | Inequality-constrained least squares Bayesian estimation Minimax estimation Non-linear programming Aggregate constraint method |
| 本文献已被 SpringerLink 等数据库收录！ |
|
