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Constrained optimization. In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to ...
Project management triangle. The project management triangle (called also the triple constraint, iron triangle and project triangle) is a model of the constraints of project management. While its origins are unclear, it has been used since at least the 1950s. [1] It contends that:
Definition. The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity , subject to and . Here represents the number of instances of item to include ...
The Karush–Kuhn–Tucker theorem is sometimes referred to as the saddle-point theorem. [1] The KKT conditions were originally named after Harold W. Kuhn and Albert W. Tucker, who first published the conditions in 1951. [2] Later scholars discovered that the necessary conditions for this problem had been stated by William Karush in his master ...
Lagrange multiplier. In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables ). [ 1]
The minimum-cost flow problem ( MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network. A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some capacity and cost associated.
Reduced cost. In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase for maximization problem, decrease for minimization problem) before it would be possible for a corresponding variable to assume a positive value in the optimal solution. It is the ...
Linear–quadratic regulator. The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the main results in the theory is that the ...