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I think this is an OR/LP/optimization concept you want, right? Sage includes interfaces to several such programs, including CPLEX (though I don't know how comprehensive it is), and has cvxopt as a standard package. See for instance the cvxopt documentation for more details about convex optimization, which says the following:

The linear inequality is a generalized inequality with respect to a proper convex cone. It may include componentwise vector inequalities, second-order cone inequalities, and linear matrix inequalities.

So hopefully that would be a good option. Scipy is also included, and may have some of what you are looking for.

In addition, we'd welcome additional help integrating the resources these programs bring to Sage, if you find you are interested in this!

I think this is an OR/LP/optimization concept you want, right? Sage includes interfaces to several such programs, including CPLEX (though I don't know how comprehensive it is), and has cvxopt as a standard package. See for instance the cvxopt documentation for more details about convex optimization, which says the following:

The linear inequality is a generalized inequality with respect to a proper convex cone. It may include componentwise vector inequalities, second-order cone inequalities, and linear matrix inequalities.

So hopefully that would be a good option. More info about the Sage interface is here.

Scipy is also included, and may have some of what you are looking for. for, as may GLPK, which may not yet be standard (I can't recall, though it's been discussed recently).

In addition, we'd welcome additional help integrating the resources these programs bring to Sage, if you find you are interested in this!