I want to address a particular issue I see in the comments: the (important) distinction between punishments and consequences. Punishments are distinct from consequences, and work differently. Many theories of parenting rely on consequences solely, and do not rely on punishments at all. Punishments do not inherently contain violence per se, but they do require an authoritarian system - ie, an authority (the parent) imposing the punishment. Many of the criticisms of punishment do not rely on the violence aspect, but on that authoritarian mindset, and on the fact that punishments simply teach aversion to punishment. Having consequences for actions, rather than punishments, will tend to be entirely nonviolent, and does not necessarily rely on authoritarianism.
Below, some additional details not directly necessary but possibly helpful in understanding the distinction.
In general, punishment is either inflicting a negative state or removing a positive state that is not connected to the behavior or action being punished. Hitting a child, yelling at the child, and sending him to his room are punishments; so are the following:
Johnny, you didn't do your homework, so you are grounded for the rest of the week.
Jane, you played video games when you were supposed to be doing your homework, so you can't go to the mall on Saturday with your friends.
So, in fact, is this:
Alan, you were talking on the phone with Jason instead of doing your homework, so I'm cutting off your phone privileges until tomorrow.
All of these are punishments: A did/did not happen, so now I am imposing B. Punishments are inherently authoritarian - they are imposed by the parent based on their authority - and are reactive; something happened in the past, so (punishment). They are often inherently unpredictable (not necessarily that a punishment might occur, but the specific punishment) and tend to teach the child to avoid punishment rather than any specific lesson.
This is different from consequences: consequences logically follow from the action. They may or may not be imposed from above; when they are, they are clearly explained and still logically follow from the action.
Johnny, you didn't finish your homework in time to watch TV, so you don't have time to watch TV tonight.
Jane, your video games obviously are distracting you from doing your homework, so you'll need to finish that before you play any more.
Alan, if you keep talking on the phone with Jason instead of doing your homework, you'll need to check your phone into the charging dock until you finish.
Those aren't really all that difference from the first set, but they are directly, logically consequent from the choices the children made earlier: Johnny knows he must finish his homework before he watches TV, so he can't watch TV if he doesn't finish his homework before his show is on. Jane's parents observe that video games are distracting Jane from finishing her homework, and so apply a similar constraint; the same basic idea applies in Alan's case.
All of these are still fundamentally authoritarian, of course; but I think it's not on topic for this question to go into that aspect here. Suffice to say consequences like the above are not violent in any way: the child knows the direct consequence of his action, which is logically associated with his choice. (Of course, there is a more obvious consequence for all three of these actions: failing a grade in school, which many children would well understand to be a consequence of their action in any event.)