A class of non-convex functions
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What are some examples of not necessarily convex functions mapping $mathbb{R}^n rightarrow mathbb{R}$ which are smooth, have gradients of bounded norm and have a global/local minima? I would be delighted see some non-trivial non-oscillating parametric families of such functions!
The easiest examples of this type that I can think of are $sin$ and $cos$.
optimization convex-optimization nonlinear-optimization
asked Nov 18 at 22:24
gradstudent
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What are some examples of not necessarily convex functions mapping $mathbb{R}^n rightarrow mathbb{R}$ which are smooth, have gradients of bounded norm and have a global/local minima? I would be delighted see some non-trivial non-oscillating parametric families of such functions!
The easiest examples of this type that I can think of are $sin$ and $cos$.
optimization convex-optimization nonlinear-optimization
asked Nov 18 at 22:24
gradstudent
18517
Any arctangent function fits this description.
– probably_someone
Nov 18 at 23:13
Sorry! I had a typo. Please see the question now.
– gradstudent
Nov 18 at 23:52
Any arctangent function restricted to $[a,infty)$ for finite $a<0$ fits this description.
– probably_someone
Nov 18 at 23:54
I do not want to bound the domain. I am always thinking of functions defined on the whole R^n
– gradstudent
Nov 18 at 23:55
Then that should also be a requirement.
– probably_someone
Nov 18 at 23:55
|
show 6 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What are some examples of not necessarily convex functions mapping $mathbb{R}^n rightarrow mathbb{R}$ which are smooth, have gradients of bounded norm and have a global/local minima? I would be delighted see some non-trivial non-oscillating parametric families of such functions!
The easiest examples of this type that I can think of are $sin$ and $cos$.
optimization convex-optimization nonlinear-optimization
asked Nov 18 at 22:24
gradstudent
18517
What are some examples of not necessarily convex functions mapping $mathbb{R}^n rightarrow mathbb{R}$ which are smooth, have gradients of bounded norm and have a global/local minima? I would be delighted see some non-trivial non-oscillating parametric families of such functions!
The easiest examples of this type that I can think of are $sin$ and $cos$.
optimization convex-optimization nonlinear-optimization
optimization convex-optimization nonlinear-optimization
asked Nov 18 at 22:24
gradstudent
18517
asked Nov 18 at 22:24
gradstudent
18517
edited Nov 19 at 0:06
asked Nov 18 at 22:24
gradstudent
18517
asked Nov 18 at 22:24
gradstudent
18517
asked Nov 18 at 22:24
gradstudent
18517
18517
Any arctangent function fits this description.
– probably_someone
Nov 18 at 23:13
Sorry! I had a typo. Please see the question now.
– gradstudent
Nov 18 at 23:52
Any arctangent function restricted to $[a,infty)$ for finite $a<0$ fits this description.
– probably_someone
Nov 18 at 23:54
I do not want to bound the domain. I am always thinking of functions defined on the whole R^n
– gradstudent
Nov 18 at 23:55
Then that should also be a requirement.
– probably_someone
Nov 18 at 23:55
|
show 6 more comments
Any arctangent function fits this description.
– probably_someone
Nov 18 at 23:13
Sorry! I had a typo. Please see the question now.
– gradstudent
Nov 18 at 23:52
Any arctangent function restricted to $[a,infty)$ for finite $a<0$ fits this description.
– probably_someone
Nov 18 at 23:54
I do not want to bound the domain. I am always thinking of functions defined on the whole R^n
– gradstudent
Nov 18 at 23:55
Then that should also be a requirement.
– probably_someone
Nov 18 at 23:55
Any arctangent function fits this description.
– probably_someone
Nov 18 at 23:13
Any arctangent function fits this description.
– probably_someone
Nov 18 at 23:13
Sorry! I had a typo. Please see the question now.
– gradstudent
Nov 18 at 23:52
Sorry! I had a typo. Please see the question now.
– gradstudent
Nov 18 at 23:52
Any arctangent function restricted to $[a,infty)$ for finite $a<0$ fits this description.
– probably_someone
Nov 18 at 23:54
Any arctangent function restricted to $[a,infty)$ for finite $a<0$ fits this description.
– probably_someone
Nov 18 at 23:54
I do not want to bound the domain. I am always thinking of functions defined on the whole R^n
– gradstudent
Nov 18 at 23:55
I do not want to bound the domain. I am always thinking of functions defined on the whole R^n
– gradstudent
Nov 18 at 23:55
Then that should also be a requirement.
– probably_someone
Nov 18 at 23:55
Then that should also be a requirement.
– probably_someone
Nov 18 at 23:55
|
show 6 more comments
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Any arctangent function fits this description.
– probably_someone
Nov 18 at 23:13
Sorry! I had a typo. Please see the question now.
– gradstudent
Nov 18 at 23:52
Any arctangent function restricted to $[a,infty)$ for finite $a<0$ fits this description.
– probably_someone
Nov 18 at 23:54
I do not want to bound the domain. I am always thinking of functions defined on the whole R^n
– gradstudent
Nov 18 at 23:55
Then that should also be a requirement.
– probably_someone
Nov 18 at 23:55