KKT conditions - Equality constraints
$begingroup$
I have an equality constraints as
$qquad qquad min_x f(x) \ qquad qquad s.t. quad Ax leq b \qquad qquad qquad x = h(x)$.
The KKT conditions of the minimization without the equality constraints is
$qquad qquad nabla f(x) + A^T u = 0, Ax < b \ qquad qquad u geq 0 quad &quad u^TAx = 0$.
Can I replace $x = H(x)$ in the above KKT conditions, and assume that the equality constraints are also satisfied?
convex-optimization nonlinear-optimization karush-kuhn-tucker
asked Jan 3 at 19:02
Majid MohammadiMajid Mohammadi
275
$endgroup$
add a comment |
$begingroup$
I have an equality constraints as
$qquad qquad min_x f(x) \ qquad qquad s.t. quad Ax leq b \qquad qquad qquad x = h(x)$.
The KKT conditions of the minimization without the equality constraints is
$qquad qquad nabla f(x) + A^T u = 0, Ax < b \ qquad qquad u geq 0 quad &quad u^TAx = 0$.
Can I replace $x = H(x)$ in the above KKT conditions, and assume that the equality constraints are also satisfied?
convex-optimization nonlinear-optimization karush-kuhn-tucker
asked Jan 3 at 19:02
Majid MohammadiMajid Mohammadi
275
$endgroup$
2
$begingroup$
After replacing $x=h(x)$ you still have $x$ left in the objective that must satisfy the constraint, so no.
$endgroup$
– A.Γ.
Jan 3 at 20:23
add a comment |
$begingroup$
I have an equality constraints as
$qquad qquad min_x f(x) \ qquad qquad s.t. quad Ax leq b \qquad qquad qquad x = h(x)$.
The KKT conditions of the minimization without the equality constraints is
$qquad qquad nabla f(x) + A^T u = 0, Ax < b \ qquad qquad u geq 0 quad &quad u^TAx = 0$.
Can I replace $x = H(x)$ in the above KKT conditions, and assume that the equality constraints are also satisfied?
convex-optimization nonlinear-optimization karush-kuhn-tucker
asked Jan 3 at 19:02
Majid MohammadiMajid Mohammadi
275
$endgroup$
I have an equality constraints as
$qquad qquad min_x f(x) \ qquad qquad s.t. quad Ax leq b \qquad qquad qquad x = h(x)$.
The KKT conditions of the minimization without the equality constraints is
$qquad qquad nabla f(x) + A^T u = 0, Ax < b \ qquad qquad u geq 0 quad &quad u^TAx = 0$.
Can I replace $x = H(x)$ in the above KKT conditions, and assume that the equality constraints are also satisfied?
convex-optimization nonlinear-optimization karush-kuhn-tucker
convex-optimization nonlinear-optimization karush-kuhn-tucker
asked Jan 3 at 19:02
Majid MohammadiMajid Mohammadi
275
asked Jan 3 at 19:02
Majid MohammadiMajid Mohammadi
275
asked Jan 3 at 19:02
Majid MohammadiMajid Mohammadi
275
asked Jan 3 at 19:02
Majid MohammadiMajid Mohammadi
275
asked Jan 3 at 19:02
Majid MohammadiMajid Mohammadi
275
275
2
$begingroup$
After replacing $x=h(x)$ you still have $x$ left in the objective that must satisfy the constraint, so no.
$endgroup$
– A.Γ.
Jan 3 at 20:23
add a comment |
2
$begingroup$
After replacing $x=h(x)$ you still have $x$ left in the objective that must satisfy the constraint, so no.
$endgroup$
– A.Γ.
Jan 3 at 20:23
2
2
$begingroup$
After replacing $x=h(x)$ you still have $x$ left in the objective that must satisfy the constraint, so no.
$endgroup$
– A.Γ.
Jan 3 at 20:23
$begingroup$
After replacing $x=h(x)$ you still have $x$ left in the objective that must satisfy the constraint, so no.
$endgroup$
– A.Γ.
Jan 3 at 20:23
add a comment |
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$begingroup$
After replacing $x=h(x)$ you still have $x$ left in the objective that must satisfy the constraint, so no.
$endgroup$
– A.Γ.
Jan 3 at 20:23