引用本文: 谢建, 龙四春, 周璀. 不等式约束PEIV模型的最优性条件及SQP算法[J]. 武汉大学学报 ( 信息科学版), 2020, 45(7): 1002-1007.
XIE Jian, LONG Sichun, ZHOU Cui. Optimality Conditions of Inequality Constrained Partial EIV Model and the SQP Algorithm[J]. Geomatics and Information Science of Wuhan University, 2020, 45(7): 1002-1007.
 Citation: XIE Jian, LONG Sichun, ZHOU Cui. Optimality Conditions of Inequality Constrained Partial EIV Model and the SQP Algorithm[J]. Geomatics and Information Science of Wuhan University, 2020, 45(7): 1002-1007.

## Optimality Conditions of Inequality Constrained Partial EIV Model and the SQP Algorithm

• 摘要: 基于约束非线性规划理论的最优性条件，推导了不等式约束PEIV(partial errors-in-variables)模型在加权最小二乘准则下取得最优解的一阶必要条件和二阶充分条件，以此作为算法设计的依据和检核解最优性的标准。根据序列二次规划算法，将非线性目标函数和约束方程在近似值处用泰勒级数展开，转换为二次规划子问题，采用积极约束算法同时估计模型参数和系数阵元素。数值模拟算例和线性回归的结果表明，新算法可行有效，具有良好的计算效率。

Abstract: According to the optimality conditions of constrained nonlinear programming theory, the first-order necessary conditions and the second-order sufficient conditions of the weighted least squares solution are derived in inequality constrained partial errors-in-variables model. These conditions are used to design the algorithms and check the optimality of the solution. The nonlinear target function is expanded to the second order at the approximate value with Taylor series and a quadratic programming sub-problem is formed based on the method of sequential quadratic programming. The model parameters and elements of the coefficient matrix are calculated with active set method at the same time. The data simulation and a linear regression example show that the new algorithm is feasible and effective, which is more efficient than the linea- rization method.

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