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Nesterov's paper Smooth minimization of non-smooth functions

Regarding Nesterov's smooth minimizationCan a smooth convex functions be non-differentiable?Interesting examples of convex non smooth funcionsBounded Quadratic Concave MinimizationWhat I am missing in this simple equation from Nesterov's paper?Solving an Energy Minimization Problem, as Outlined in a Paperlower complexity bounds for problems with smooth functions (Nesterov's Lectures 2004)Why is the Nesterov's accelerated gradient different for convex and strongly convex functions?A necessary and sufficient condition for optimality of non-smooth convex functions over convex setUnderstanding minimization of jointly convex functions

2

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I was reading Nesterov's famous paper Smooth minimization of non-smooth functions. I got stuck in the first line of Theorem 3's proof. According to the paper, inequality (4.5) should be a direct result from Theorem 2. However I failed to see where $frac1(N+1)^2$ in the first term of right-hand side comes from. Shouldn't it be $frac4(N+1)(N+2)$?

---

---

---

It should be a simple arithmetic manipulation. But I cannot figure it out after hours of thinking. I hope anyone familiar with this paper could explain it to me. Thanks in advance!

optimization convex-analysis proof-explanation convex-optimization

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edited 23 hours ago

Alex Ravsky

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2

$begingroup$

I was reading Nesterov's famous paper Smooth minimization of non-smooth functions. I got stuck in the first line of Theorem 3's proof. According to the paper, inequality (4.5) should be a direct result from Theorem 2. However I failed to see where $frac1(N+1)^2$ in the first term of right-hand side comes from. Shouldn't it be $frac4(N+1)(N+2)$?

---

---

---

It should be a simple arithmetic manipulation. But I cannot figure it out after hours of thinking. I hope anyone familiar with this paper could explain it to me. Thanks in advance!

optimization convex-analysis proof-explanation convex-optimization

share|cite|improve this question

edited 23 hours ago

Alex Ravsky

42.6k32383

asked 2 days ago

LooopsLooops

113

New contributor

Looops is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

I was reading Nesterov's famous paper Smooth minimization of non-smooth functions. I got stuck in the first line of Theorem 3's proof. According to the paper, inequality (4.5) should be a direct result from Theorem 2. However I failed to see where $frac1(N+1)^2$ in the first term of right-hand side comes from. Shouldn't it be $frac4(N+1)(N+2)$?

---

---

---

It should be a simple arithmetic manipulation. But I cannot figure it out after hours of thinking. I hope anyone familiar with this paper could explain it to me. Thanks in advance!

optimization convex-analysis proof-explanation convex-optimization

share|cite|improve this question

edited 23 hours ago

Alex Ravsky

42.6k32383

asked 2 days ago

LooopsLooops

113

New contributor

Looops is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited 23 hours ago

Alex Ravsky

42.6k32383

asked 2 days ago

LooopsLooops

113

New contributor

Looops is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited 23 hours ago

Alex Ravsky

42.6k32383

asked 2 days ago

LooopsLooops

113

New contributor

Looops is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited 23 hours ago

Alex Ravsky

42.6k32383

edited 23 hours ago

Alex Ravsky

42.6k32383

asked 2 days ago

LooopsLooops

113

New contributor

Looops is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 days ago

LooopsLooops

113