Existence of solution

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This pertains to whether a mathematical program has a solution. One source of non-existence is that the feasible region is empty. Another is that it is unbounded, and it is possible to have a sequence of feasible points whose objective value diverges. In linear programming, these are the only sources of non-existence. In nonlinear programming, however, we can have asymptotes such that the objective is bounded but cannot achieve its infimum or supremum. See the Bolzano-Weierstrass theorem, which is fundamental. For linear programming, see theorems of the alternative.


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