We consider relative or subjective optimization problems where the goal function and feasible set are dependent on 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. Preliminary results of computational experiments confirmed efficiency of the proposed method.

我们考虑相对或主观的优化问题，其中目标函数和可行集取决于所考虑系统的当前状态。通常，将它们表述为准平衡问题，因此很难找到解决方案。我们描述了度量空间中的一类相当普遍的相对优化问题，此外，该问题还取决于起始状态。我们还利用这些问题的准平衡型公式，表明它们接受了相当简单的下降解决方法。这种方法给出了趋于相对最佳状态的合适轨迹。我们描述了这些问题的几个应用示例。计算实验的初步结果证实了该方法的有效性。