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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. [1] It is used most often to compare two numbers on the number line by their size.
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.
Inequation. In mathematics, an inequation is a statement that an inequality holds between two values. [1][2] It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific inequality relation. Some examples of inequations are:
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Cauchy–Schwarz inequality. The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) [1][2][3][4] is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is considered one of the most important and widely used inequalities in mathematics.
Lagrange multiplier. In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1]
Main parameters and notation. The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c; the semiperimeter s = (a + b + c) / 2 (half the perimeter p); the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as ...
Bhatia–Davis inequality, an upper bound on the variance of any bounded probability distribution. Bernstein inequalities (probability theory) Boole's inequality. Borell–TIS inequality. BRS-inequality. Burkholder's inequality. Burkholder–Davis–Gundy inequalities. Cantelli's inequality. Chebyshev's inequality.
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