0
votes
0answers
38 views

minimum distance between sets and relation with functions [on hold]

Let $A, B$ be two convex and closed subsets of $\mathbb{R}^n$. We would like to the minimum distance between these two sets. i.e., we want to find a solution for the following problem. $$ \min ...
2
votes
5answers
187 views

Distance between two sets

Let $A, B$ be two convex and closed subsets of $\mathbb{R}^n$. We would like to the minimum distance between these two sets. i.e., we want to find a solution for the following problem. $$ \min ...
2
votes
2answers
265 views

convergence of the infima of convex functions

Can one give a reference to a result like this: If a sequence of convex functions $f_{n}$ on $\mathbb{R}$ converges pointwise to a non-monotonic function $f$, then ...
1
vote
0answers
86 views

Subgradient of Minimum Eigenvalue

Consider three $N \times N$ hermitian matrices $A_0,A_1,A_2$. Consider the function \begin{align} f(t_1,t_2)=\lambda_{min}(A_0+t_1A_1+t_2A_2) \end{align} where $\lambda_{min}$ denotes the minimum ...