There is no "gun violence", there is only criminal behavior.
To control criminal behavior there are a number of measures that, taken together, would reduce crime to the minimum that fallen human nature permits.
#1. Permit, even encourage, all sane, adult, non-felons to arm themselves -- either concealed carry or open carry -- with their choice of gun, sword, knife, pepper spray, taser, etc.
#2. Honor, rather than prosecute, those who shoot criminals who invade their homes and/or threaten their lives or the lives of those around them.
#3. Stop "catch and release policing". Ensure that criminals actually serve their sentences.
#4. Determine immigration status of all persons arrested and turn those who are illegally in the country over to the appropriate authorities for swift deportation.
#5. Encourage a cultural reformation towards the values that build up rather than tear down civilization. Things such as personal responsibility, industry, thrift, family, patriotism, honor, faithfulness, virtue, persistence, personal integrity, ... -- the pursuit of the highest and the best rather than the lowest common denominator.
The last is the most necessary and the most difficult since it cannot come from without but must take hold in the hearts and minds of each individual. But taking the High Road as a society and culture can be encouraged.