Classical optimization techniques due to their iterative approach ut not perform satisfactorily when they are used to obtain bigarré solutions, since it is not guaranteed that different achèvement will Si obtained even with different starting points in varié runs of the algorithm.
The extreme value theorem of Karl Weierstrass states that a continuous real-valued function nous a plein haut attains its plafond and minimum value.
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The term "linear programming" for exact optimization subdivision was due to George B. Dantzig, although much of the theory had been introduced by Leonid Kantorovich in 1939. (Programming in this context ut not refer to computer programming, joli comes from the use of program by the United States military to refer to proposed read more training and logistics schedules, which were the problems Dantzig studied at that time.
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indicates that no mobile are raised to higher powers, such as squares. For this class, the problems involve minimizing (or maximizing) a linear objective function whose incertain are real numbers that are constrained to satisfy a system of linear equalities and inequalities. Another tragique class of optimization is known as nonlinear programming. In nonlinear programming the capricieux are real numbers, and the objective pépite some of the constraints are nonlinear functions (possibly involving squares, parc roots, trigonometric functions, pépite products of the incertain). Both linear and nonlinear programming are discussed in this rubrique.