Branches of Mathematics
Optimization
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Optimization is the branch of mathematics concerned with selecting the best element, according to some measurable criterion, from a set of available alternatives, and with the methods for finding it efficiently.
Facts
Central QuestionGiven a criterion to maximize or minimize and a set of allowed choices, does a best choice exist, and can it be found or verified without checking every alternative in turn. 1 Key DebateHow much structure a problem needs before its best solution can be certified rather than merely searched for. The Simplex algorithm, published in 1947, gave a practical method for linear problems, and John von Neumann's work on the theory of duality around the same time showed that a linear program and a related dual program can certify each other's optimal value, a guarantee that most harder, nonlinear optimization problems still lack. 1 Cross-Tradition Connections
Sources
1. Wikipedia: Mathematical Optimization
Wikimedia FoundationLead sectionQuote, Lead section
the selection of a best element, with regard to some criteria, from some set of available alternatives
1. Wikipedia: Mathematical Optimization
Wikimedia FoundationSufficient conditions for optimality sectionQuote, Sufficient conditions for optimality section
If a candidate solution satisfies the first-order conditions, then the satisfaction of the second-order conditions as well is sufficient to establish at least local optimality.
1. Wikipedia: Mathematical Optimization
Wikimedia FoundationHistory sectionQuote, History section
Dantzig published the Simplex algorithm in 1947, and also John von Neumann and other researchers worked on the theoretical aspects of linear programming (like the theory of duality) around the same time.
Stone-Weierstrass Theorem (Wikipedia)
Wikipedialead paragraphQuote, lead paragraph
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.
Stone-Weierstrass Theorem (Wikipedia)
WikipediaHistory sectionQuote, History section
Dantzig published the Simplex algorithm in 1947, and also John von Neumann and other researchers worked on the theoretical aspects of linear programming (like the theory of duality) around the same time.
Wikipedia: Minimax Theorem
Wikimedia FoundationIncludes: Minimax Theorem, Lead sectionQuote, Includes: Minimax Theorem, Lead section
In the mathematical area of game theory and of convex optimization
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