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Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization , some or all of the variables used in a discrete optimization problem are restricted to be discrete variables —that is, to assume only a discrete set of values, such as the integers .
An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found.
In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
In continuous optimization, A is some subset of the Euclidean space R n, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. In combinatorial optimization, A is some subset of a discrete space, like binary strings, permutations, or sets of integers.
In mathematics, in the area of numerical analysis, Galerkin methods are a family of methods for converting a continuous operator problem, such as a differential equation, commonly in a weak formulation, to a discrete problem by applying linear constraints determined by finite sets of basis functions.
Discrete vs. continuous. A discrete model treats objects as discrete, such as the particles in a molecular model or the states in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe flows, temperatures and stresses in a solid, and electric field that applies ...
Continuous optimization is a branch of optimization in applied mathematics. [ 1 ] As opposed to discrete optimization , the variables used in the objective function are required to be continuous variables —that is, to be chosen from a set of real values between which there are no gaps (values from intervals of the real line ).
On the other hand, discrete choice analysis examines situations in which the potential outcomes are discrete, such that the optimum is not characterized by standard first-order conditions. Thus, instead of examining "how much" as in problems with continuous choice variables, discrete choice analysis examines "which one".