We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem involving $l_1$ vector norm with a positive semidefinite cone constraint. By utilizing convex optimization theory, we rewrite its first order optimality condition as a generalized equation. Under extremely simple assumptions, we prove that any element of the generalized Jacobian of the equation at its solution is nonsingular. Based on this, we construct an inexact Newton method with Armijo line search to solve the equation and demonstrate its global convergence. Finally, we report the numerical results illustrating effectiveness of the Newton methods.

中文翻译：

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逆二次规划问题 \ begin {document} $ l_1 $ \ end {document} 规范措施

我们考虑一个逆二次规划（QP）问题，其中对给定QP问题的目标函数中的参数进行尽可能少的调整，以使已知的可行解决方案成为最佳解决方案。我们将此问题表述为涉及带有正半定锥约束的$ l_1 $向量范数的最小化问题。利用凸优化理论，将其一阶最优条件重写为广义方程。在极其简单的假设下，我们证明方程方程组的广义雅可比行列式的任何元素都是非奇异的。在此基础上，我们利用Armijo线搜索构造了一种不精确的牛顿法来求解方程并证明其全局收敛性。最后，我们报告了数值结果，说明了牛顿法的有效性。