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mathematical_optimization [2014/09/23 12:04]
sertalpbilal created 		mathematical_optimization [2024/04/24 03:38] (current)
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 ====== Mathematical Optimization ====== ====== Mathematical Optimization ======
  
-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.1411488281.txt.gz · Last modified: 1998/12/03 12:11 (external edit)

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