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The objective function of a linear Support Vector Machine (SVM) in machine learning can be given by,

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where,:

• w⁽ⁱ⁾ represents the weight associated with each training example.
• h_θ(x⁽ⁱ⁾) is the hypothesis function, which is the output for input x⁽ⁱ⁾ using parameters θ.
• y⁽ⁱ⁾ is the true label of the training example x⁽ⁱ⁾.
• 1{h_θ(x⁽ⁱ⁾) = y (i)} is an indicator function that equals 1 if the predicted output (h_θ(x⁽ⁱ⁾)) matches the true label (y⁽ⁱ⁾), and 0 otherwise.
• a(θ): This is the objective function that the algorithms aim to maximize. The objective is to find the hyperplane that maximally separates the data points of different classes.
• This sum part of the equation is a summation over all training examples (i).

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