Unbounded solution of LPP

Question

In connection with LPP, what is meant by 'unbounded solution' and 'unbounded objective function'? Are they same or they are distinct concepts?

Answer 1

It depends on what you mean by solution. Are solutions optimal or just feasible? Unfortunately, the terminology varies.

Unbound objective function just means that the objective function is unbounded on the feasible set. That is, there is a sequence of feasible points (some called them solutions) with unbounded objective values. Since the feasible set is closed and the objective is continuous, at least one component must be unbounded.

Unbounded solutions, in sense of feasible points, do not imply unbounded objective function, as for example the direction could be orthogonal to vector (gradient) of the objective function.