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I am solving about constrained optimization problem.

To solve this, I have to find conditions that satisfy KKT condition.

From KKT condition, I got matrix equation like $(A+bB)x=C$.

Here, $A$ and $B$ are square symmetric matrix and invertible. $b$ is scalar value.

I want to solve this theoretically.

Can I express $(A+bB)^{-1}$ with $A, B, b, A^{-1}$, and $B^{-1}$?

TShiong
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ikchae
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    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Dec 27 '22 at 11:48
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    It does not exist when $A=B=1, b=-1$. – geetha290krm Dec 27 '22 at 11:52
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    Possible duplicate https://math.stackexchange.com/questions/17776/inverse-of-the-sum-of-matrices – user326159 Dec 27 '22 at 11:55

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