论文标题
一类相对优化问题的一般类
A General Class of Relative Optimization Problems
论文作者
论文摘要
我们考虑相对或主观优化问题，其中目标函数和可行集合取决于所考虑的系统的当前状态。通常，它们被称为准平衡问题，因此找到其解决方案可能很困难。我们描述了度量空间中相当一般的相对优化问题类别，此外，这取决于起始状态。我们还利用了这些问题的准平衡类型公式，并表明它们承认了相当简单的下降溶液方法。这种方法提供了适合相对最佳状态的轨迹。我们描述了这些问题应用的几个示例。
We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence finding their solutions may be rather difficult. We describe a rather general class of relative optimization problems in metric spaces, which in addition depend on the starting state. We also utilize quasi-equilibrium type formulations of these problems and show that they admit rather simple descent solution methods. This approach gives suitable trajectories tending to a relatively optimal state. We describe several examples of applications of these problems.
