Minimizimi

Minimizimi is the Albanian term for minimization, referring to the process of reducing a quantity to its smallest possible value or size. It is used in everyday language, as well as in formal disciplines such as mathematics, computer science, economics, and engineering.

In mathematics and optimization, a minimization problem asks to find an argument x in a feasible set X that minimizes an objective function f(x). A global minimum is the smallest value attained over X, while a local minimum is the smallest in a neighborhood. If f is convex on a convex set X, any local minimum is a global minimum, ensuring uniqueness under strict convexity or other conditions.

Algorithms for minimization include gradient descent and its variants for differentiable f, coordinate descent, Newton or quasi-Newton methods, and specialized solvers for linear and convex problems. In nonconvex problems, heuristics such as simulated annealing or genetic algorithms may be used.

In computer science, minimization also refers to reducing code size or resource consumption, such as minification of JavaScript or CSS to reduce bandwidth, or minimizing memory and energy use in software systems.

In economics and operations research, minimization concerns reducing costs, losses, or risks, often under constraints.