We consider problems of linear copositive programming where feasible sets consist of vectors for which the quadratic forms induced by the corresponding linear matrix combinations are nonnegative over the nonnegative orthant. Given a linear copositive problem, we define immobile indices of its constraints and a normalized immobile index set. We prove that the normalized immobile index set is either empty or can be represented as a union of a finite number of convex closed bounded polyhedra. We show that the study of the structure of this set and the connected properties of the feasible set permits to obtain new optimality criteria for copositive problems. These criteria do not require the fulfillment of any additional conditions (constraint qualifications or other). An illustrative example shows that the optimality conditions formulated in the paper permit to detect the optimality of feasible solutions for which the known sufficient optimality conditions are not able to do this. We apply the approach based on the notion of immobile indices to obtain new formulations of regularized primal and dual problems which are explicit and guarantee strong duality.

中文翻译：

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线性共正规划问题的固定指标和无CQ最优准则

我们考虑线性共积规划的问题，其中可行集由向量组成，对于这些向量，由相应的线性矩阵组合诱导的二次形式在非负正整数上为非负。给定一个线性共正问题，我们定义其约束的固定索引和一个标准化的固定索引集。我们证明归一化的固定索引集为空或可以表示为有限数量的凸封闭有界多面体的并集。我们表明，对该集合的结构和可行集合的连通性质的研究允许获得针对正问题的新的最优性准则。这些标准不需要满足任何其他条件（约束资格或其他条件）。一个说明性的例子表明，本文中提出的最优性条件允许检测可行解决方案的最优性，而已知的最优性条件对此不可行。我们应用基于不动指数概念的方法来获得正则化原始问题和对偶问题的新表述，这些问题是明确的并保证强对偶性。