Assuming this is a linear programming problem, .... it is fairly elementary. LP has an implicit non-negativity constraint, right? Xj >= 0. So, if you want Xj >= Lj you can redefine your problem with Xj - Lj >=0.Let X"j = Xj - Lj.
See also page 78-79 in Bradley/Hax/Magnanti Applied Mathematical Programming.
I don't really understand the question. Is there any objective to optimize? What is the problem you're actually trying to solve? I think that some indications are missing here...
But, provided you have a linear objective function, as the constaints are linear, I would suggest using Dantzig's simplex method or any of its variants (dual, 2-phase, etc.). The special structure of the constraints should allow to solve the problem quite easily.
Assuming your problem is a linear optimization...
You may redefine the problem and "shift" the bounds to zero.
This will alter the right-hand-side in the problem
and require a constant term in the (linear) objective.
In fact, this constraint can appear in any mathematical programming model, both in linear and nonlinear cases. Many softwares exist to solve this kind of models, especially Cplex and Lingo whose the demo versions are available.
I suggest you to explore the column generation procedure. It might help you to develop an efficient algorithm. Good luck.
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