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mathematical_optimization [2014/09/24 12:31]
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mathematical_optimization [2024/03/14 11:26] (current)
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 In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.((The Nature of Mathematical Programming, Mathematical Programming Glossary, INFORMS Computing Society.)) In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.((The Nature of Mathematical Programming, Mathematical Programming Glossary, INFORMS Computing Society.))
  
-In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.+In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains..
  
 ===== Optimization Problems ===== ===== Optimization Problems =====
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 represents the $(x,y)$ pair (or pairs) that maximizes (or maximize) the value of the objective function $x\cos(y)$, with the added constraint that $x$ lie in the interval $[-5,5]$ (again, the actual maximum value of the expression does not matter). In this case, the solutions are the pairs of the form $(5, 2k\pi)$ and $(−5,(2k+1)\pi)$, where $k$ ranges over all integers. represents the $(x,y)$ pair (or pairs) that maximizes (or maximize) the value of the objective function $x\cos(y)$, with the added constraint that $x$ lie in the interval $[-5,5]$ (again, the actual maximum value of the expression does not matter). In this case, the solutions are the pairs of the form $(5, 2k\pi)$ and $(−5,(2k+1)\pi)$, where $k$ ranges over all integers.
  
-**Arg min** and **arg max** are sometimes also written **argmin** and **argmax**, and stand for argument of the minimum and argument of the maximum.+**Arg min** and **arg max** are sometimes also written **argmin** and **argmax**, and stand for argument of the minimum and argument of the maximum.[[http://btseducation.edu.vn|du hoc he]]
  
mathematical_optimization.1411576298.txt.gz · Last modified: 1998/12/03 12:11 (external edit)