Some possibilities in R can be found here:

https://www.google.com/search?rlz=1C1CHBF_enUS847US847&biw=1600&bih=827&ei=7utcXfjNHcyMtgXWuY6wDA&q=sensitivity+analysis+tools+r&oq=sensitivity+analysis+tools+r&gs_l=psy-ab.3..33i22i29i30l10.29598.30249..31184...0.2..0.117.197.1j1......0....1..gws-wiz.......0i71j0j0i22i30j0i22i10i30.AQC3BL73-CI&ved=0ahUKEwj4_J74sZPkAhVMhq0KHdacA8Y4ChDh1QMICg&uact=5

But is this ols regression, another kind of optimization say some kind of Math Programming ,a simulation or???

@David Eugene Booth

First I want to explore the input parameters and see what interactions, correlations they have, and how large is their effect on the dependent variables. Then, I'm going to find some optimized combinations of the input variables. I'm aware that there are many R packages for Sensitivity Analysis but I'm looking for the specific assumptions explained in the question: not normally distributed data; categorical input variables, correlated input variables.

You can do a univariate sensitivity analysis where you vary parameters one at a time and observe the effect on output values. Test the least certain parameters or those that produce the widest range of output values

@Andrew Paul McKenzie Pegman

One factor at a time approach has been widely criticized as it doesn't take into account the probable interactions between different variables.

Aryan Shahabian The assumptions change as the methods change as the problem changes. In my experience, sensitivity analysis was about how a solution to a problem changes as the input conditions or input data or ... change. It might help you to consider what a sensitivity analysis on the methods in one or the other of the attached papers might mean. IMO this is especially interesting because adaptive lasso in both of these situations has an oracle property as is mentioned. Best wishes, David Booth