Non-linear constrained problem transformation to equivalent un-constrained problem
I have the following non-linear optimization problem:
min $f(x, y, z) = x + y + z$
s.t.
$x^2 + y = 3$
$x + 3y + 2z = 7$
Is there a way to transform this problem to an equivalent minimisation problem without any constraints?
I have a hunch that it has something to do with Lagrange multipliers but I really can't figure out how to start this one.
Thanks,
Louis
optimization nonlinear-optimization lagrange-multiplier
asked Nov 28 at 16:53
Louis-Philippe Noël
123
add a comment |
I have the following non-linear optimization problem:
min $f(x, y, z) = x + y + z$
s.t.
$x^2 + y = 3$
$x + 3y + 2z = 7$
Is there a way to transform this problem to an equivalent minimisation problem without any constraints?
I have a hunch that it has something to do with Lagrange multipliers but I really can't figure out how to start this one.
Thanks,
Louis
optimization nonlinear-optimization lagrange-multiplier
asked Nov 28 at 16:53
Louis-Philippe Noël
123
add a comment |
I have the following non-linear optimization problem:
min $f(x, y, z) = x + y + z$
s.t.
$x^2 + y = 3$
$x + 3y + 2z = 7$
Is there a way to transform this problem to an equivalent minimisation problem without any constraints?
I have a hunch that it has something to do with Lagrange multipliers but I really can't figure out how to start this one.
Thanks,
Louis
optimization nonlinear-optimization lagrange-multiplier
asked Nov 28 at 16:53
Louis-Philippe Noël
123
I have the following non-linear optimization problem:
min $f(x, y, z) = x + y + z$
s.t.
$x^2 + y = 3$
$x + 3y + 2z = 7$
Is there a way to transform this problem to an equivalent minimisation problem without any constraints?
I have a hunch that it has something to do with Lagrange multipliers but I really can't figure out how to start this one.
Thanks,
Louis
optimization nonlinear-optimization lagrange-multiplier
optimization nonlinear-optimization lagrange-multiplier
asked Nov 28 at 16:53
Louis-Philippe Noël
123
asked Nov 28 at 16:53
Louis-Philippe Noël
123
asked Nov 28 at 16:53
Louis-Philippe Noël
123
asked Nov 28 at 16:53
Louis-Philippe Noël
123
asked Nov 28 at 16:53
Louis-Philippe Noël
123
123
add a comment |
add a comment |
1 Answer
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Guide:
We have $y=3-x^2$, that is whenever we see $y$, we can replace it by $3-x^2$.
Also, we can express $z$ as a function of $x$ and $y$.
Hence yes, we just have to perform a substitution to replace everything in terms of $x$.
The unconstrained problem is a quadratic minimization problem.
answered Nov 28 at 16:56
Siong Thye Goh
98.4k1463116
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Guide:
We have $y=3-x^2$, that is whenever we see $y$, we can replace it by $3-x^2$.
Also, we can express $z$ as a function of $x$ and $y$.
Hence yes, we just have to perform a substitution to replace everything in terms of $x$.
The unconstrained problem is a quadratic minimization problem.
answered Nov 28 at 16:56
Siong Thye Goh
98.4k1463116
add a comment |
Guide:
We have $y=3-x^2$, that is whenever we see $y$, we can replace it by $3-x^2$.
Also, we can express $z$ as a function of $x$ and $y$.
Hence yes, we just have to perform a substitution to replace everything in terms of $x$.
The unconstrained problem is a quadratic minimization problem.
answered Nov 28 at 16:56
Siong Thye Goh
98.4k1463116
add a comment |
Guide:
We have $y=3-x^2$, that is whenever we see $y$, we can replace it by $3-x^2$.
Also, we can express $z$ as a function of $x$ and $y$.
Hence yes, we just have to perform a substitution to replace everything in terms of $x$.
The unconstrained problem is a quadratic minimization problem.
answered Nov 28 at 16:56
Siong Thye Goh
98.4k1463116
Guide:
We have $y=3-x^2$, that is whenever we see $y$, we can replace it by $3-x^2$.
Also, we can express $z$ as a function of $x$ and $y$.
Hence yes, we just have to perform a substitution to replace everything in terms of $x$.
The unconstrained problem is a quadratic minimization problem.
answered Nov 28 at 16:56
Siong Thye Goh
98.4k1463116
answered Nov 28 at 16:56
Siong Thye Goh
98.4k1463116
answered Nov 28 at 16:56
Siong Thye Goh
98.4k1463116
answered Nov 28 at 16:56
Siong Thye Goh
98.4k1463116
98.4k1463116
add a comment |
add a comment |
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