引用本文: 谢雪梅, 宋迎春, 夏玉国. 区间约束平差模型的共轭梯度积极集算法[J]. 武汉大学学报 ( 信息科学版), 2019, 44(9): 1274-1281.
XIE Xuemei, SONG Yingchun, XIA Yuguo. An Active Set Algorithm of Conjugate Gradients for Adjustment Model with Interval Constraints[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1274-1281.
 Citation: XIE Xuemei, SONG Yingchun, XIA Yuguo. An Active Set Algorithm of Conjugate Gradients for Adjustment Model with Interval Constraints[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1274-1281.

## An Active Set Algorithm of Conjugate Gradients for Adjustment Model with Interval Constraints

• 摘要: 主要研究参数带有区间约束的平差算法，通过把平差问题转化成一个带有区间约束的二次规划问题，利用积极集对二次规划问题进行划分与重组，结合无约束共轭梯度优化算法，给出了带有区间约束的平差算法，并同时给出了参数解的精度评估。由于投影梯度法可以迅速改变积极约束集的构成，新的算法比经典的积极集法效率更高，可以降低模型的不适定性，保持参数先验信息中的统计、几何或物理意义，适合于求解大规模的带有区间约束的平差问题。

Abstract: This paper mainly studies the adjustment model with interval constraints, in which the adjustment problem is transformed into a quadratic programming problem with interval constraints. A new adjustment algorithm with interval constraints is presented, and the accuracy of the parameter solution is evaluated, in which the active set algorithm and unconstrained conjugate gradient optimization algorithm are used to partition and reconstruct the quadratic problems. Because the projection gradient method can rapidly change the composition of the active constraint set, the new algorithm is more efficient than the classical active set method, which can reduce the uncertainty of the model, and maintain the statistical, geometric or physical meaning of priori information, and is suitable for solving large-scale adjustment problems with interval constraints.

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