minimas

Minimas is a form that appears in English as a plural of minimum in mathematical usage. The standard plural forms are minima and minimums; minimas is less common and often arises from translation or casual use. In general, a minimum is the smallest value attained by a function, sequence, or set on a given domain. Minima can be classified as local (relative to a neighborhood) or global (the smallest over the entire domain).

Local minima occur at points where the function value is not greater than nearby points, while global minima are the absolute smallest values on the whole domain. Minima can also be strict, where the function is strictly larger at every nearby point, or non-strict (flat) near the minimum. Endpoints of a domain may produce boundary minima, which are minima attained at boundary points rather than interior ones.

Locating minima typically involves calculus or optimization techniques. For a differentiable single-variable function, critical points occur where the derivative is zero or undefined, and a second-derivative test can indicate a local minimum when the second derivative is positive. In several variables, one looks for points where the gradient is zero and analyzes the Hessian matrix; a positive-definite Hessian indicates a strict local minimum. Convex functions have the additional property that any local minimum is global. Numerical methods such as gradient descent or Newton’s method are commonly used to approximate minima when closed-form solutions are not available.

Minima appear across disciplines: in optimization as targets to minimize cost or energy, in physics as energy minima, and in economics as cost or disutility minima. In mathematical writing, minima is the standard plural form; minimas remains rare and is typically encountered in informal or cross-linguistic contexts.