# Optimization Landscape **Domain:** Optimization / Machine Learning **Doc Type:** Technical Concept Node **Maturity:** Foundational ## Definition An **optimization landscape** is the geometric picture formed by an objective function over possible parameter or solution states. Peaks, valleys, plateaus and saddle regions describe how local changes alter the objective. ## Technical Context The landscape metaphor makes the limits of local search visible. [[wiki/Gradient Descent|Gradient descent]] follows local derivative information, while the structure of the landscape determines whether that path reaches a globally preferred solution or a [[wiki/Local Optimum|local optimum]]. ## Historical Context [[wiki/Shun-Ichi Amari|Shun-Ichi Amari]] discussed non-global local minima in 1967, and [[wiki/Geoffrey Hinton|Geoffrey Hinton]] answered the standing local-maxima objection for a particular feasible space in his 1977 thesis. ## See Also [[wiki/Optimization|Optimization]], [[wiki/Stochastic Gradient Descent|Stochastic Gradient Descent]], [[wiki/Objective Function|Objective Function]]