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How to show that solution for the maximum margin hyperplane for hard-margin SVM is unchanged when w.x + b = (+/-) 1 is replaced by arbitrary constant $\gamma$?

In the derivation for the SVM, we generally assume that the margin boundaries are given by w.x + b = +1 and w.x+b = −1.

Can we show that if the +1 and -1 on the right-hand side were replaced by some arbitrary constants +$\gamma$ and −$\gamma$ where $\gamma$ > 0, the solution for the maximum margin hyperplane will remain unchanged?

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  • $\begingroup$ Here's a hint - Let $S_\gamma = \left\{(w_\gamma, b_\gamma)\right\}$ be the solution set when solving with a given $\gamma > 0$. Prove that $S_\gamma = \gamma S_1$ by contradiction. $\endgroup$
    – MotiNK
    Oct 10, 2021 at 7:08

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