论文标题
关于优化问题的双重功能的强大凹陷
On the strong concavity of the dual function of an optimization problem
论文作者
论文摘要
我们提供了三个新的证据，证明了某些凸优化问题的双重功能的强大凹度。对于非线性约束的问题，我们表明，物镜的强凸度的假设不能削弱至凸度，并且假设最佳解决方案处所有约束的梯度是线性独立的，则不能进一步削弱。最后，我们用几个示例来说明结果。
We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened to convexity and that the assumption that the gradients of all constraints at the optimal solution are linearly independent cannot be further weakened. Finally, we illustrate our results with several examples.
