We consider infinite programming problems with constraint sets defined by systems of infinite number of inequalities and equations given by continuously differentiable functions defined on Banach spaces. In the approach proposed here we represent these systems with the help of coefficients in a given Schauder basis. We prove Abadie constraint qualification under the new infinite-dimensional Relaxed Constant Rank Constraint Qualification Plus and we discuss the existence of Lagrange multipliers via Hurwicz set. The main tools are: Rank Theorem and Lyusternik–Graves theorem.

中文翻译：

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无限规划问题的 Schauder 基础约束条件

我们考虑无限规划问题，其约束集由无限数量的不等式系统定义，方程由巴纳赫空间上定义的连续可微函数给出。在这里提出的方法中，我们借助给定 Schauder 基中的系数来表示这些系统。我们证明了新的无限维松弛常秩约束资格Plus下的Abadie约束资格，并通过Hurwicz集讨论了拉格朗日乘子的存在性。主要工具有：Rank定理和Lyusternik-Graves定理。