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  2. Cauchy–Schwarz inequality - Wikipedia

    en.wikipedia.org/wiki/Cauchy–Schwarz_inequality

    Cauchy–Schwarz inequality (Modified Schwarz inequality for 2-positive maps [27]) — For a 2-positive map between C*-algebras, for all , in its domain, () ‖ ‖ (), ‖ ‖ ‖ ‖ ‖ ‖. Another generalization is a refinement obtained by interpolating between both sides of the Cauchy–Schwarz inequality:

  3. Constraint satisfaction - Wikipedia

    en.wikipedia.org/wiki/Constraint_satisfaction

    Variable elimination and the simplex algorithm are used for solving linear and polynomial equations and inequalities, and problems containing variables with infinite domain. These are typically solved as optimization problems in which the optimized function is the number of violated constraints.

  4. Fourier–Motzkin elimination - Wikipedia

    en.wikipedia.org/wiki/Fourier–Motzkin_elimination

    Redundant constraint can be identified by solving a linear program as follows. Given a linear constraints system, if the -th inequality is satisfied for any solution of all other inequalities, then it is redundant. Similarly, STIs refers to inequalities that are implied by the non-negativity of information theoretic measures and basic ...

  5. Poincaré inequality - Wikipedia

    en.wikipedia.org/wiki/Poincaré_inequality

    When Ω is a ball, the above inequality is called a (p,p)-Poincaré inequality; for more general domains Ω, the above is more familiarly known as a Sobolev inequality. The necessity to subtract the average value can be seen by considering constant functions for which the derivative is zero while, without subtracting the average, we can have ...

  6. Mathematical optimization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_optimization

    Typically, A is some subset of the Euclidean space, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. The domain A of f is called the search space or the choice set, while the elements of A are called candidate solutions or feasible solutions.

  7. Ladyzhenskaya's inequality - Wikipedia

    en.wikipedia.org/wiki/Ladyzhenskaya's_inequality

    The original such inequality, for functions of two real variables, was introduced by Ladyzhenskaya in 1958 to prove the existence and uniqueness of long-time solutions to the Navier–Stokes equations in two spatial dimensions (for smooth enough initial data). There is an analogous inequality for functions of three real variables, but the ...

  8. Domain (mathematical analysis) - Wikipedia

    en.wikipedia.org/wiki/Domain_(mathematical_analysis)

    In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C. For example, the entire complex plane is a domain, as is the open unit disk, the open upper half-plane, and so forth. Often, a complex domain serves as the domain of definition for a holomorphic function.

  9. List of inequalities - Wikipedia

    en.wikipedia.org/wiki/List_of_inequalities

    Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution

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