论文标题
Slater条件没有内部点的lebesgue空间中的程序，界定界定且有限的许多约束
Slater conditions without interior points for programs in Lebesgue spaces with pointwise bounds and finitely many constraints
论文作者
论文摘要
我们考虑在Lebesgue空间中具有点重框约束的优化问题，并有限许多其他线性约束。我们证明，严格存在于点的界限和满足线性约束的平面点的存在足以满足拉格朗日乘数的存在。令人惊讶的是，从某种意义上说，拉格特点也是Lagrange乘数的必要条件。我们还演示了如何处理其他有限的许多非线性约束。
We consider optimization problems in Lebesgue spaces with pointwise box constraints and finitely many additional linear constraints. We prove that the existence of a Slater point which lies strictly between the pointwise bounds and which satisfies the linear constraints is sufficient for the existence of Lagrange multipliers. Surprisingly, the Slater point is also necessary for the existence of Lagrange multipliers in a certain sense. We also demonstrate how to handle additional finitely many nonlinear constraints.
