<p>This <a href="http://www.princeton.edu/%7Eyc5/ele522_optimization/lectures/subgradient_methods.pdf" rel="nofollow noreferrer">lecture note</a> gives the proof for how deterministic subgradient method converges on non-smooth convex and strongly convex Lipschitz functions.</p>
<p>Is there a non-convex version of this proof?</p>
<p>Like convergence of subgradient method for,</p>
<ul>
<li>non-smooth Lipschitz non-convex functions (like <span class="math-container">$\frac{1}{1+e^{-\vert x \vert}}$</span>) ?</li>
<li>non-smooth non-Lipschitz non-convex functions (like <span class="math-container">$(1-\vert x \vert)^2$</span>)?</li>
</ul>
<p>(happy to get references for the the stochastic versions of these too!)</p>

CC BY-SA 4.0
2021-03-23T04:35:38.550Z
On non-smooth optimization, better ask at Math SE, I would guess. There's a tag for it there.
Rodrigo de Azevedo
CC BY-SA 4.0
2021-03-23T04:54:47.460Z
Okay. If I dont get answers in a couple of days, I will move it there :D
gradstudent
<optimization>
Convergence of first order subgradient methods for non-convex functions
gradstudent
# Convergence of first order subgradient methods for non-convex functions

(Asked by: username_0 on 2021-03-23)

This [lecture note](http://www.princeton.edu/%7Eyc5/ele522_optimization/lectures/subgradient_methods.pdf) gives the proof for how deterministic subgradient method converges on non-smooth convex and strongly convex Lipschitz functions.

Is there a non-convex version of this proof?

Like convergence of subgradient method for,

* non-smooth Lipschitz non-convex functions (like $\frac{1}{1+e^{-\vert x \vert}}$) ?
* non-smooth non-Lipschitz non-convex functions (like $(1-\vert x \vert)^2$)?

(happy to get references for the the stochastic versions of these too!)

**Tags:** optimization

> **Comments:**
> **username_1**: On non-smooth optimization, better ask at Math SE, I would guess. There's a tag for it there.  
> **username_0**: Okay. If I dont get answers in a couple of days, I will move it there :D  

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## 0 answers

