Mixing
Unbounded solution of LPP
$begingroup$
In connection with LPP, what is meant by 'unbounded solution' and 'unbounded objective function'? Are they same or they are distinct concepts?
linear-programming
asked Mar 16 '16 at 10:38
user3575652user3575652
87112
$endgroup$
add a comment |
$begingroup$
In connection with LPP, what is meant by 'unbounded solution' and 'unbounded objective function'? Are they same or they are distinct concepts?
linear-programming
asked Mar 16 '16 at 10:38
user3575652user3575652
87112
$endgroup$
$begingroup$
What is LPP? ${}{}$
$endgroup$
– user251257
Mar 16 '16 at 13:46
$begingroup$
Linear programming problem
$endgroup$
– user3575652
Mar 17 '16 at 3:46
add a comment |
$begingroup$
In connection with LPP, what is meant by 'unbounded solution' and 'unbounded objective function'? Are they same or they are distinct concepts?
linear-programming
asked Mar 16 '16 at 10:38
user3575652user3575652
87112
$endgroup$
In connection with LPP, what is meant by 'unbounded solution' and 'unbounded objective function'? Are they same or they are distinct concepts?
linear-programming
linear-programming
asked Mar 16 '16 at 10:38
user3575652user3575652
87112
asked Mar 16 '16 at 10:38
user3575652user3575652
87112
asked Mar 16 '16 at 10:38
user3575652user3575652
87112
asked Mar 16 '16 at 10:38
user3575652user3575652
87112
asked Mar 16 '16 at 10:38
user3575652user3575652
87112
87112
$begingroup$
What is LPP? ${}{}$
$endgroup$
– user251257
Mar 16 '16 at 13:46
$begingroup$
Linear programming problem
$endgroup$
– user3575652
Mar 17 '16 at 3:46
add a comment |
$begingroup$
What is LPP? ${}{}$
$endgroup$
– user251257
Mar 16 '16 at 13:46
$begingroup$
Linear programming problem
$endgroup$
– user3575652
Mar 17 '16 at 3:46
$begingroup$
What is LPP? ${}{}$
$endgroup$
– user251257
Mar 16 '16 at 13:46
$begingroup$
What is LPP? ${}{}$
$endgroup$
– user251257
Mar 16 '16 at 13:46
$begingroup$
Linear programming problem
$endgroup$
– user3575652
Mar 17 '16 at 3:46
$begingroup$
Linear programming problem
$endgroup$
– user3575652
Mar 17 '16 at 3:46
add a comment |
1 Answer
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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.
answered Mar 17 '16 at 4:46
user251257user251257
7,52721128
$endgroup$
add a comment |
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1 Answer
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1 Answer
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active
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$begingroup$
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.
answered Mar 17 '16 at 4:46
user251257user251257
7,52721128
$endgroup$
add a comment |
$begingroup$
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.
answered Mar 17 '16 at 4:46
user251257user251257
7,52721128
$endgroup$
add a comment |
$begingroup$
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.
answered Mar 17 '16 at 4:46
user251257user251257
7,52721128
$endgroup$
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.
answered Mar 17 '16 at 4:46
user251257user251257
7,52721128
answered Mar 17 '16 at 4:46
user251257user251257
7,52721128
answered Mar 17 '16 at 4:46
user251257user251257
7,52721128
answered Mar 17 '16 at 4:46
user251257user251257
7,52721128
7,52721128
add a comment |
add a comment |
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$begingroup$
What is LPP? ${}{}$
$endgroup$
– user251257
Mar 16 '16 at 13:46
$begingroup$
Linear programming problem
$endgroup$
– user3575652
Mar 17 '16 at 3:46