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Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [ 1 ] [ 2 ] It is generally divided into two subfields: discrete optimization and continuous optimization .
The use of optimization software requires that the function f is defined in a suitable programming language and connected at compilation or run time to the optimization software. The optimization software will deliver input values in A , the software module realizing f will deliver the computed value f ( x ) and, in some cases, additional ...
For each combinatorial optimization problem, there is a corresponding decision problem that asks whether there is a feasible solution for some particular measure m 0. For example, if there is a graph G which contains vertices u and v, an optimization problem might be "find a path from u to v that uses the fewest edges". This problem might have ...
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).
In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions V 1, V 2, ..., V n taking y as an argument representing the state of the system at times i from 1 to n.
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as convergence rate, precision, robustness and general performance.
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.
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] It is named after the mathematician Joseph-Louis ...