First, a few assumptions:
1. You created a "settings" object called "mySettings" to hold the min and max properties values.
2. You created a converter() function that, among other things, gets the min and max properties values and assigns them to mySettings.
3. In your enumerateObjectInstances() implementation, when handling the VisualObjectInstance object that has the min and max properties, you assign it with the corresponding values from mySettings.
The general idea is as follows:
In your converter() function, after you get the min and max values, you compare them to see if max is greater than min. If it is, than you assign their values to mySettings as usual. Otherwise, you set the invalid value to a valid one in mySettings(E.g, you can set min to max-1, or set max to min+1, or even check to see which one had its value changed and set it to its previous value, and so on...).
You can also notify the user about the error that occured by using the hostServices.setWarnings() method in your update() method. You can find many usage examples in the custom visuals github project(One example can be found in the funnelChart.ts file's update() implementation). This method pops up that annoying Power BI error message dialog.