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2. Inequality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Inequality_(mathematics)

   The feasible regions of linear programming are defined by a set of inequalities. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. The main types of inequality are less than and ...

3. Fourier–Motzkin elimination - Wikipedia

   en.wikipedia.org/wiki/Fourier–Motzkin_elimination

   Fourier–Motzkin elimination. Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph Fourier [1] who proposed the method in 1826 and Theodore Motzkin who re-discovered it in 1936.

4. AM–GM inequality - Wikipedia

   en.wikipedia.org/wiki/AM–GM_inequality

   Visual proof that (x + y)2 ≥ 4xy. Taking square roots and dividing by two gives the AM–GM inequality. [1] In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same ...

5. Linear inequality - Wikipedia

   en.wikipedia.org/wiki/Linear_inequality

   Linear inequality. In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: [1] < less than. > greater than. ≤ less than or equal to. ≥ greater than or equal to. ≠ not equal to. A linear inequality looks exactly like a linear equation, with the ...

6. Chebyshev's inequality - Wikipedia

   en.wikipedia.org/wiki/Chebyshev's_inequality

   Chebyshev's inequality. In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation of a random variable (with finite variance) from its mean. More specifically, the probability that a random variable deviates from its mean by more than is at most ...

7. Nesbitt's inequality - Wikipedia

   en.wikipedia.org/wiki/Nesbitt's_inequality

   Nesbitt's inequality. In mathematics, Nesbitt's inequality, named after Alfred Nesbitt, states that for positive real numbers a, b and c , There is no corresponding upper bound as any of the 3 fractions in the inequality can be made arbitrarily large. It is the three-variable case of the rather more difficult Shapiro inequality, and was ...

8. Rearrangement inequality - Wikipedia

   en.wikipedia.org/wiki/Rearrangement_inequality

   Rearrangement inequality. In mathematics, the rearrangement inequality [1] states that for every choice of real numbers. and every permutation of the numbers we have. . (1) Informally, this means that in these types of sums, the largest sum is achieved by pairing large values with large values, and the smallest sum is achieved by pairing small ...

9. Variational inequality - Wikipedia

   en.wikipedia.org/wiki/Variational_inequality

   Variational inequality. In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini ...