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visits member for 2 years, 9 months
seen Oct 10 at 1:47

Oct
3
comment Will continuous extension preserve strict convexity?
This function is not even convex. You can consider $g(x)=h(x,x)=(x^2-1)^2$.
Oct
3
asked Will continuous extension preserve strict convexity?
Sep
21
accepted Is the limit point of this sequence unique?
Sep
21
comment Is the limit point of this sequence unique?
Great. I'd better pick up a book and review some basics.
Sep
21
comment Is the limit point of this sequence unique?
Thanks for your quick response. Please see my edit.
Sep
21
revised Is the limit point of this sequence unique?
added 48 characters in body
Sep
21
asked Is the limit point of this sequence unique?
Sep
15
comment normal cone to sublevel set
Without the assumption that ${\rm cone}\,\partial f(\bar{x})$ is closed, why is the inclusion $N_C(\bar{x})\subset{\rm cone}\,\partial f(\bar{x})$ equivalent to $(N_C(\bar{x}))^{\circ}\supset({\rm cone}\,\partial f(\bar{x}))^{\circ}$?
Sep
15
comment normal cone to sublevel set
This is indeed an exercise in Borwein's book: Convex analysis and nonlinear optimization. Although it is an exercise, I think it is very useful to relate many stuff together. As I mentioned, it appears in many other textbooks as a theorem in a bit different form.
Sep
15
comment normal cone to sublevel set
Moreover, I do not think a direction polar to all subgradients has to be a descent direction. Consider $f(x,y)=\frac{1}{2}(x^2+y^2)$ at $(1,0)$. The gradient is $(1,0)$. The direction $(0,1)$ is polar to $(1,0)$ and belong to the tangent cone. But it is indeed an ascent direction. Please let me know if I miss anything. Thanks.
Sep
15
comment normal cone to sublevel set
Hi, gerw: could you please provide more detail about the last inequality? By the way, I think you also make use of the fact that ${\rm cone}\,\partial f(\bar{x})$ is closed. Thus, it is the same as $({\rm cone}\,\partial f(\bar{x}))^{\circ\circ}$. This is due to $0\notin\partial f(\bar{x})$. Am I right? Thanks a lot.
Sep
13
asked normal cone to sublevel set
Sep
1
accepted Is the smallest singular value able to measure the similarity between two matrices?
Jul
2
awarded  Curious
Apr
19
comment Please explain the intuition behind the dual problem in optimization.
Terrific explanation. Many thanks.
Apr
16
revised Is the smallest singular value able to measure the similarity between two matrices?
added 88 characters in body
Apr
16
comment Is the smallest singular value able to measure the similarity between two matrices?
Sorry for the confusion. (a) $A$ and $B$ are not necessarily square matrices. (b) span $B$ means the column space of $B$.
Apr
15
awarded  Yearling
Apr
15
asked Is the smallest singular value able to measure the similarity between two matrices?
Oct
18
accepted Integrate $\int_0^{\pi/2}\frac{\sin^3t}{\sin^3t+\cos^3t}dt$?