for γ ∈ R + {\displaystyle \gamma \in \mathbb {R} _{+}} small enough, then F ( a n ) ≥ F ( a n + 1 ) {\displaystyle F(\mathbf {a_{n}} )\geq F(\mathbf {a_{n+1}} )} . In other words, the term γ ∇ F ( a ) {\displaystyle \gamma \nabla F(\mathbf {a} )} is subtracted from a {\displaystyle \mathbf {a} } because we want to move against the gradient, toward the local minimum. With this observation in mind, one starts with a guess x 0 {\displaystyle \mathbf {x} _{0}} for a local minimum of F {\displaystyle F} , and considers the sequence x 0 , x 1 , x 2 , … {\displaystyle \mathbf {x} _{0},\mathbf {x} _{1},\mathbf {x} _{2},\ldots } such that