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I am interested in the gradient system

$$\dot{x}(t)=-\nabla f(x(t))$$

where $f:\mathbb{R}^n \to \mathbb{R}$ is a $C^{1,1}$ function (that is, a differentiable function whose gradient is Lipschitz continuous). I would be grateful if someone could propose some reference books related to this system.

Rodrigo de Azevedo
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Blind
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1 Answers1

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If $f$ is convex, then the gradient flow $\dot{x} = - \nabla f (x)$ is doing continuous-time gradient descent. A book on gradient flows is the following one:

Rodrigo de Azevedo
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  • @Blind Page 20 of the book (page 31 of the PDF file). – Rodrigo de Azevedo May 27 '16 at 21:54
  • Do you reccomend more references. I am grateful to you if you could give your comments on the following question: http://math.stackexchange.com/questions/1802541/elementary-properties-of-gradient-systems – Blind May 28 '16 at 15:36