maksimeer

Maksimeer is an Estonian verb meaning to maximize, i.e., to increase an objective value to its greatest possible amount under given constraints. The term is commonly used in mathematics, optimization, economics, and computer science to describe the act of seeking the highest attainable value of a function or variable.

In practice, maksimeer refers to the process of finding argument values that yield the maximum of an objective function. This can occur in unconstrained problems, where one seeks critical points by setting the derivative to zero and checking second-order conditions, or in constrained problems, where feasible solutions must satisfy restrictions. The term is often used together with related concepts such as "maksimum" (the maximum value itself or the point at which it occurs) and is contrasted with "minimeer" (to minimize).

Methods for maksimeer vary by problem type. In calculus, techniques include gradient or Hessian analysis to locate maxima. In constrained optimization, Lagrange multipliers provide a way to incorporate constraints into the optimization. In convex or concave settings, certain guarantees hold: maximizing a concave function over a convex set yields a global maximum; in linear programming, maximizing a linear objective over a polyhedron yields an optimal solution at a vertex. Computational methods such as gradient ascent, interior-point methods, branch-and-bound, and heuristic approaches are also used for larger or discrete problems.

Examples include maximizing profit in economics, maximizing utility in consumer theory, or maximizing a linear objective in resource allocation. Maksimeer thus denotes a fundamental operation across disciplines that study optimal decisions under limitations.