George Assaad

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Hi there! I am an aspiring machine learning (ML) researcher who loves to tinker with deep learning models to make them more fun.

I hope to join a great Ph.D. program next this year (I did).

You can find my contact info to reach out down below.

I can’t think of more to add to the description. So, here is the Karush–Kuhn–Tucker (KKT) conditions¹ until I find the optimal one.

\[\begin{aligned} min_{x \in \mathbb{R}^n} \ & f(x) \\ \text{subject to } & c_i(x) = 0,\quad i \in \mathcal{E} \textit{ (the equality constraints)} \\ & c_i(x) \geq 0,\quad i \in \mathcal{I} \textit{ (the inequality constraints)} \\ \end{aligned}\]

Suppose that $x^*$ is a local solution, that the functions $f$ and $c_i$ are continuously differentiable, and that the LICQ holds at $x^∗$.

Then there is a Lagrange multiplier vector $ \lambda^∗$, such that the following conditions are satisfied at $(x^∗, \lambda^∗)$:

\[\begin{aligned} \nabla f(x^∗) - \sum_{i \in \mathcal{E} \cup \mathcal{I} } \lambda^*_i \nabla c_i(x^*) &= 0, \\ c_i(x^*) &= 0,\quad \text{ for all } i \in \mathcal{E} \\ c_i(x^*) &\geq 0,\quad \text{ for all } i \in \mathcal{I} \\ \lambda^*_i &\geq 0,\quad \text{ for all } i \in \mathcal{I} \\ \lambda^*_i c_i(x^*) &= 0,\quad \text{ for all } i \in \mathcal{E} \cup \mathcal{I} \\ \end{aligned}\]

Notes

• The photo in the homepage is taken in front of The Berlin Victory Column. I highly recommend visiting Berlin.