This paper is concerned with the inexact variable metric method for solving convex-constrained optimization problems. At each iteration of this method, the search direction is obtained by inexactly minimizing a strictly convex quadratic function over the closed convex feasible set. Here, we propose a new inexactness criterion for the search direction subproblems. Under mild assumptions, we prove that any accumulation point of the sequence generated by the new method is a stationary point of the problem under consideration. In order to illustrate the practical advantages of the new approach, we report some numerical experiments. In particular, we present an application where our concept of the inexact solutions is quite appealing.

本文关注求解凸约束优化问题的不精确变量度量方法。在该方法的每次迭代中，搜索方向是通过在闭凸可行集上不精确地最小化严格凸二次函数来获得的。在这里，我们为搜索方向子问题提出了一个新的不精确标准。在温和的假设下，我们证明了新方法生成的序列的任何累积点都是所考虑问题的驻点。为了说明新方法的实际优势，我们报告了一些数值实验。特别是，我们提出了一个应用程序，其中我们的不精确解决方案的概念非常吸引人。