Conceptual

Gradient Descent Direction via Negative Gradient Vector Computation

The core principle dictates that in unconstrained optimization within Euclidean space, the direction of steepest descent for a differentiable scalar function is defined by the negative gradient vector at a given point. This mechanism relies on the formal application of partial derivatives and the chain rule to construct an ascent-descent path orthogonal to level sets of the objective function. It represents a fundamental first-order iterative method within numerical optimization theory, serving as the foundational update rule for minimizing differentiable loss landscapes in continuous domains.