SVM using hinge loss function to maximize margin with gradient descent wont converge

Question

I am implementing an SVM and to find the largest margin, I am using a hinge loss cost function like this from this article, but I am implementing it myself. So far I have come up with this, which produces odd values when predicting from my data set, which is indeed linearly separable (my x_train is a 2D array and y_train is a 1D array with the binary split into -1 or 1)

def SVM(x_train, y_train, w="RANDOM", epochs=1000000, learning_rate=0.00001):
    if w == "RANDOM":
        w = []
        for i in range(len(x_train[0])):
            w.append(random.random())
        w = np.array(w)

    for i in range(epochs):
        y_pred = w.dot(x_train[0])
        prod = y_pred * y_train

        l = 0
        for val in prod:
            if val >= -1:
                for n in range(len(w)):
                    w[n] = w[n] - learning_rate * 2 * 1/epochs * w[n]
            else:
                for n in range(len(w)):
                    w[n] = w[n] + learning_rate * (y_train[l] * x_train[l][n] - 2 * 1/epochs * w[n])
            l += 1
    return w


def cost_function(y, y_pred):
    return 1 - y * y_pred

I suspect my problem lies within the prediction and not the correction as I think I have understood gradient descent decently enough to implement it. prod = y_pred * y_train is the part you subtract from 1 in the cost function without soft-margin but why do we have to iterate through its elements? That's something that the article does in its code. In addition, I'm unsure whether predicting y based on only one element from x_train makes sense for training the AI.