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  2. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    The definition of global minimum point also proceeds similarly. If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗.

  3. Mathematical optimization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_optimization

    The extreme value theorem of Karl Weierstrass states that a continuous real-valued function on a compact set attains its maximum and minimum value. More generally, a lower semi-continuous function on a compact set attains its minimum; an upper semi-continuous function on a compact set attains its maximum point or view.

  4. Maximum theorem - Wikipedia

    en.wikipedia.org/wiki/Maximum_theorem

    The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The statement was first proven by Claude Berge in 1959. [1] The theorem is primarily used in mathematical economics and optimal control.

  5. Utility maximization problem - Wikipedia

    en.wikipedia.org/wiki/Utility_maximization_problem

    The mathematical first order conditions for a maximum of the consumer problem guarantee that the demand for each good is homogeneous of degree zero jointly in nominal prices and nominal wealth, so there is no money illusion. When the prices of goods change, the optimal consumption of these goods will depend on the substitution and income effects.

  6. Maximal and minimal elements - Wikipedia

    en.wikipedia.org/wiki/Maximal_and_minimal_elements

    The maximum of a subset of a preordered set is an element of which is greater than or equal to any other element of , and the minimum of is again defined dually. In the particular case of a partially ordered set , while there can be at most one maximum and at most one minimum there may be multiple maximal or minimal elements.

  7. Arg max - Wikipedia

    en.wikipedia.org/wiki/Arg_max

    As an example, both unnormalised and normalised sinc functions above have of {0} because both attain their global maximum value of 1 at x = 0. The unnormalised sinc function (red) has arg min of {−4.49, 4.49}, approximately, because it has 2 global minimum values of approximately −0.217 at x = ±4.49.

  8. Banker's algorithm - Wikipedia

    en.wikipedia.org/wiki/Banker's_algorithm

    Banker's algorithm is a resource allocation and deadlock avoidance algorithm developed by Edsger Dijkstra that tests for safety by simulating the allocation of predetermined maximum possible amounts of all resources, and then makes an "s-state" check to test for possible deadlock conditions for all other pending activities, before deciding whether allocation should be allowed to continue.

  9. Supply and demand - Wikipedia

    en.wikipedia.org/wiki/Supply_and_demand

    Supply chain as connected supply and demand curves. In microeconomics, supply and demand is an economic model of price determination in a market.It postulates that, holding all else equal, the unit price for a particular good or other traded item in a perfectly competitive market, will vary until it settles at the market-clearing price, where the quantity demanded equals the quantity supplied ...