The concepts of immobile indices and their immobility orders are objective and important characteristics of feasible sets of semi-infinite programming (SIP) problems. They can be used for the formulation of new efficient optimality conditions without constraint qualifications. Given a class of convex SIP problems with polyhedral index sets, we describe and justify a finite constructive algorithm (algorithm DIIPS) that allows to find in a finite number of steps all immobile indices and the corresponding immobility orders along the feasible directions. This algorithm is based on a representation of the cones of feasible directions in the polyhedral index sets in the form of linear combinations of extremal rays and on the approach proposed in our previous papers for the cases of immobile indices’ sets of simpler structures. A constructive procedure of determination of the extremal rays is described, and an example illustrating the application of the DIIPS algorithm is provided.

固定索引的概念及其固定顺序是可行的半无限规划（SIP）问题集的客观和重要特征。它们可以用于制定新的有效最优条件而无约束条件。给定一类具有多面体索引集的凸SIP问题，我们描述并证明了有限的构造算法（算法DIIPS），从而可以在有限的步骤中沿着可行方向找到所有固定索引和相应的固定顺序。该算法基于极角射线线性组合形式的多面体索引集中可行方向圆锥的表示，并且基于我们先前论文中针对固定索引的较简单结构的情况提出的方法。描述了确定末端射线的建设性程序，并提供了说明DIIPS算法应用的示例。