Discrete optimization uses only integer values for function maximization, while continuous optimization uses real numbers. Discrete optimization is divided into integer programming and combinatorial optimization, and is used in mathematics, computer science, and engineering. The choice between the two depends on the project’s goals.
Discrete optimization is a category of optimization as the concept is used in the fields of computer science and mathematics. Unlike concrete or continuous optimization, discrete optimization uses only integer rather than decimal integers to perform function maximization, which is the goal of all optimizations. Discrete optimization can be further divided into integer programming and combinatorial optimization.
Continuous optimization refers to maximizing a function with continuous real numbers ranging from set integers to all those value points that lie between them. This means that the numerical values used represent any value that can appear in both the real physical world and the abstract world of mathematics. Negative numbers are possible, as are fractions and indefinite decimals. This form of optimization is the most complex and also requires the most accurate approach to mathematical functions.
The other branch of optimization is discrete optimization. Overall, the driving purpose remains the same: to maximize the results of mathematical functions applied to computers, engineering or other fields. Unlike its continuous optimization counterpart, this type of optimization deals only with discrete numeric values. These are concrete integers, such as the number 2 or 647. While the other rung runs along the number line, this discrete rung lacks smooth transitions from one integer to another – fractions in between do not matter .
As in the field of optimization itself, discrete optimization can be divided into two categories: integer programming and combinatorial optimization. In computer science, integer programming limits the variables in a program to integers only; that is, fractions and negatives cannot enter the program. Combinatorial optimization is used in computer science and mathematics and is quite complex. It involves integrating operations and optimization solutions into different types of graphs. Because of the finite, concrete nature of discrete numeric values, graphs are never smooth, but rather emphasize the vertical and horizontal axes differences that appear between two values.
Whether or not you use continuous or discrete optimization depends entirely on the scope and goals of a particular project. Besides mathematics and computer applications, different branches of optimization could be used in engineering, business or mechanical sciences. According to the project under consideration, it may be that neither discrete nor continuous optimization is used – they are only two in a number of other optimization categories.
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