5 results about "Descent direction" patented technology

In optimization, a descent direction is a vector 𝐩∈ℝⁿ that, in the sense below, moves us closer towards a local minimum 𝐱* of our objective function f:ℝⁿ→ℝ. Suppose we are computing 𝐱* by an iterative method, such as line search. We define a descent direction 𝐩ₖ∈ℝⁿ at the kth iterate to be any 𝐩ₖ such that 〈𝐩ₖ,∇f(𝐱ₖ)〉<0, where 〈,〉 denotes the inner product. The motivation for such an approach is that small steps along 𝐩ₖ guarantee that f is reduced, by Taylor's theorem.