What's the difference between feasible and pareto optimal? Do I need to prove feasibility?
If I search for pareto optimal through Lagrange multipliers, then would this mean that it's also feasible, since it's the optimal in analytic sense?
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The notion of feasibility depends on the problem at hand. However, in general a feasible solution is such that it satisfies the constraints imposed on the system. The feasible region of the optimization problem is the set of the feasible solutions.
When solving a problem using Lagrange multipliers you include the constraints in the optimization problem. Thus your Pareto optimal solution will automatically be feasible.
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