steplength

Steplength is a term used in different fields to describe a distance or amount of movement along a direction. In optimization and numerical analysis, steplength (often denoted as alpha or t) specifies how far to move from the current point in a chosen search direction. If xk is the current point and pk is a descent direction, the next iterate is often xk+1 = xk + α pk, with α chosen by a line search or other strategy. The goal is to achieve sufficient decrease in the objective while maintaining stability; common methods include backtracking line search, Armijo conditions, and Wolfe conditions. Steplength may be constrained by bounds or by a trust-region framework, and its selection strongly influences convergence speed and robustness.

In gait analysis and biomechanics, steplength (often called step length) is the distance between successive foot contacts of the same foot, or equivalently the distance covered in one step. It is a key parameter of human walking and running, typically measured in meters and related to leg length and walking speed. Step length, along with cadence, contributes to overall gait efficiency and energy expenditure. It can be affected by aging, neurological or musculoskeletal conditions, and rehabilitation interventions. Step length is commonly estimated using motion capture systems, force plates, or wearable sensors, and is frequently analyzed alongside stride length, speed, and symmetry.

Related concepts include stride length, which is the distance covered in a full gait cycle, and learning rate, used in machine learning to describe how quickly a model adapts. While sharing a name, steplength in optimization and step length in gait analysis serve distinct purposes within their respective disciplines.