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1. Minimum

   Linked via "function (mathematics)"

   The minimum refers to the lowest possible value of a function (mathematics)/), or the point at which this lowest value is attained. It is a fundamental concept across mathematics, physics, optimization theory, and various fields of applied science, representing a state of lowest potential energy (cost, or deviation) within a defined domain. In geometric terms, a minimum often corresponds to the bottom of a valley or the lowest point on a [surface](…

2. Minimum

   Linked via "function (mathematics)"

   Mathematical Definition and Classification
   Formally, for a function (mathematics)/) $f: D \to \mathbb{R}$, where $D$ is a subset of the real numbers, a point $c \in D$ is a global minimum if $f(c) \le f(x)$ for all $x \in D$. If the inequality holds only for $x$ in some neighborhood $N$ of $c$, then $f(c)$ is a local minimum.
   Local Minima and Critical Points

3. Minimum

   Linked via "function (mathematics)"

   Computational Optimization and Iterative Methods
   The search for the minimum of a function (mathematics)/), known as minimization, is a central task in computational science, machine learning, and operations research.
   Gradient Descent