拟牛顿修正法解算不等式约束加权总体最小二乘问题

根据总体最小二乘准则，可以将附有不等式约束的变量误差（errors-in-variables，EIV）模型转化为标准最优化问题，并运用有效集法、序列二次规划法等优化方法求解。已有算法在涉及计算目标函数的Hesse矩阵（二阶导数）时，存在计算量较大的缺陷。针对上述问题，利用基于拟牛顿法修正Hesse矩阵的序列二次规划算法解算附有不等式约束加权总体最小二乘问题，新算法减小了计算量，可以提高收敛速度。通过实例，证明了该算法具有很好的适用性和计算效率。

A Quasi Newtonian Correction Algorithm for Weighted Total Least Squares Problem with Inequality Constraints

The errors-in-variables (EIV)model with inequality constraints is transformed into a standard nonlinear optimization program, which can be solved by existing optimization methods such as the active set method or sequential quadratic programming(SQP). Since weighted total least squares with inequality constraints (ICWTLS) is limited by the complexity of a Hessian matrix, which is the second partial derivative of objective function. In this paper, the Hessian matrix in SQP is replaced by an approximation based on Quasi-Newtonian method.The algorithm we propose can deal with the ICWTLS problem with a general weight matrix, and has the ability to handle large-scale problems. Eexamples illustrate that this new algorithm is efficient.