minimointiongelma
Minimointiongelma is a concept in mathematical optimization that refers to problems of finding a decision variable vector x that minimizes an objective function f(x) within a feasible set defined by constraints. The typical form is to minimize f(x) subject to x belonging to a feasible region X, where X may be specified by inequality constraints g_i(x) ≤ 0 and equality constraints h_j(x) = 0. The problem can be unconstrained (X = R^n) or constrained by bounds, relationships, or combinatorial restrictions.
Key concepts in minimointiongelma include the distinction between global and local minima. A global minimum is
Optimality conditions provide tests for candidate solutions. For unconstrained differentiable f, a necessary condition for a
Convexity plays a central role: if f is convex and the constraint set is convex, any local