The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The...

In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a power source with internal resistance...

science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink...

mapping theorem, which states that a nonconstant holomorphic function maps open sets to open sets: If | f | {\displaystyle |f|} attains a local maximum at...

In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified...

mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem and the minimum...

the maximum and minimum values of f {\displaystyle f} on the interval [ a , b ] , {\displaystyle [a,b],} which is what the extreme value theorem stipulates...

Indeed, the maximum a posteriori estimate is the parameter θ that maximizes the probability of θ given the data, given by Bayes' theorem: P ⁡ ( θ ∣ x...

In convex analysis, Danskin's theorem is a theorem which provides information about the derivatives of a function of the form f ( x ) = max z ∈ Z ϕ ( x...

have strategies. Condition 2. and 3. are satisfied by way of Berge's maximum theorem. Because u i {\displaystyle u_{i}} is continuous and compact, r ( σ...

variance, while the Fisher–Tippet–Gnedenko theorem only states that if the distribution of a normalized maximum converges, then the limit has to be one of...

extremum theorem gives only a necessary condition for extreme function values, as some stationary points are inflection points (not a maximum or minimum)...

the extreme value theorem, global maxima and minima exist. Furthermore, a global maximum (or minimum) either must be a local maximum (or minimum) in the...

discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that...

respects with those given in a discussion of the maximum-flow minimum-cut theorem. Cederbaum's theorem applies to a particular type of directed graph:...

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct...

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...

severing s from t) in the network, as stated in the max-flow min-cut theorem. The maximum flow problem was first formulated in 1954 by T. E. Harris and F....

In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation...

corresponding eigenvalue λ. The Courant minimax principle is a result of the maximum theorem, which says that for q ( x ) = ⟨ A x , x ⟩ {\displaystyle q(x)=\langle...

theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected...

contradicts the optimality of x 1 , x 2 {\displaystyle x_{1},x_{2}} . The maximum theorem implies that if: The utility function u ( x ) {\displaystyle u(x)}...

the supporting hyperplane theorem. In the context of support-vector machines, the optimally separating hyperplane or maximum-margin hyperplane is a hyperplane...

In complex analysis, Liouville's theorem, named after Joseph Liouville (although the theorem was first proven by Cauchy in 1844), states that every bounded...

Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing...

obtain the maximum satisfaction subject to buying and selling at a uniform price'. Edgeworth took a step towards the first fundamental theorem in his 'Mathematical...

In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization...

of information theory. Stated by Claude Shannon in 1948, the theorem describes the maximum possible efficiency of error-correcting methods versus levels...

Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle...

In Bayesian inference, the Bernstein–von Mises theorem provides the basis for using Bayesian credible sets for confidence statements in parametric models...