无约束逆二次规划问题
Unconstrained inverse quadratic programming problem
AI总结：
本文研究了在无约束优化框架下，通过近似最优解和目标函数值的邻域对来求解未知参数的逆二次规划问题，采用最小二乘法推导出线性方程组，并展示了其在神经计算和二次曲面拟合中的应用潜力。
摘要：
本文提出了一种无约束优化框架下的逆二次规划问题的求解方法，要求在仅知道直接问题最优解和目标函数近似值的邻域对的情况下，确定二次型矩阵和准线性部分的向量参数。该问题的求解基于最小二乘法，推导出显式形式的线性方程组，所得参数可用于重建直接二次规划问题并确定未知的最优解和目标函数极值。该方法在神经计算和二次曲面拟合等应用中具有潜在价值，并通过简单数值示例和Octave/MATLAB编程语言的实现方案进行了演示。
英文摘要：
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part of the quadratic form) provided that approximate estimates of the optimal solution of the direct problem and those of the target function to be minimized in the form of pairs of values lying in the corresponding neighborhoods are only known. The formulation of the inverse problem and its solution are based on the least squares method. In the explicit form the inverse problem solution has been derived in the form a system of linear equations. The parameters obtained can be used for reconstruction of the direct quadratic programming problem and determination of the optimal solution and the extreme value of the target function, which were not known formerly. It is possible this approach opens new ways in over applications, for example, in neurocomputing and quadric surfaces fitting. Simple numerical examples have been demonstrated. A scenario in the Octave/MATLAB programming language has been proposed for practical implementation of the method.
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