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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. [1]
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]
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 ).
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 ...
Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing.
“And I was just like, ‘Okay.’ That's, like, what's actually out in the world because of people creating hate,” she continued. “I'm a mom.
In the discrete time case, if the planning horizon is finite, the problem can also be easily solved by dynamic programming. When the underlying process is determined by a family of (conditional) transition functions leading to a Markov family of transition probabilities, powerful analytical tools provided by the theory of Markov processes can ...