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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 .
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic.
Discrete group, a group with the discrete topology; Discrete category, category whose only arrows are identity arrows; Discrete mathematics, the study of structures without continuity; Discrete optimization, a branch of optimization in applied mathematics and computer science; Discrete probability distribution, a random variable that can be counted
Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: 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 .
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.
Combinatorial optimization is the study of optimization on discrete and combinatorial objects. It started as a part of combinatorics and graph theory, but is now viewed as a branch of applied mathematics and computer science, related to operations research , algorithm theory and computational complexity theory .
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Essence of combinatorics ... Optimization Methods and Software;