求解一类二次规划反问题的同伦交替方向法

对一类带不等式约束的二次规划反问题的求解方法进行研究。首先表示出此类二次规划对应的反问题形式，将该反问题转化为目标函数变量可分离优化问题，将其中约束写成KKT条件的形式之后，该反问题等同于一个等式约束优化问题。综合以上，考虑使用交替方向乘子法进行迭代，在此基础之上，将同伦思想应用于算法每步迭代的子问题中，以此避免近端算子选取的敏感性，又可保证算法的收敛速度。针对子问题，使用逐次超松弛法进行求解，并获取算法的收敛性。最后，将该算法与SDPT3和Sedumi两种方法进行比较，数值结果表明，该算法无论在速度上还是效率上都优于以上两种方法。

A homotopy-based ADMM for a class of inverse quadratic programming problems

The solution of the inverse quadratic programming problem with inequality constraint was studied. Firstly, the form of inverse problem corresponding to this kind of quadratic programming was written, and then the inverse problem was transformed into an optimization problem with separable objective functions. After the constraints were written in the form of KKT conditions, the inverse problem was equivalent to an equality-constrained optimization problem. Based on above transformation, the alternating direction method of multipliers (ADMM) was considered for iteration. On this basis, the homotopy idea was applied to the subproblems of each iteration of our algorithm, so as to avoid the sensitivity of the selection of proximal operators and ensure the convergence speed of the algorithm. For the subproblems, the successive over-relaxation method was used to solve them, and the convergence of the algorithm was obtained. Finally, comparing the proposed method with SDPT3 and Sedumi, the results show that our algorithm is superior to the above two methods both in speed and efficiency.