mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: < less than...

v {\displaystyle \mathbf {v} } are linearly dependent. Sedrakyan's inequality, also known as Bergström's inequality, Engel's form, Titu's lemma (or the...

formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints...

In convex optimization, a linear matrix inequality (LMI) is an expression of the form LMI ⁡ ( y ) := A 0 + y 1 A 1 + y 2 A 2 + ⋯ + y m A m ⪰ 0 {\displaystyle...

{\displaystyle M} is a linear subspace then dim ⁡ ( A M ) ≤ dim ⁡ ( M ) {\displaystyle \dim(AM)\leq \dim(M)} ; apply this inequality to the subspace defined...

function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP)...

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...

rest of the sample by linear inequality, with high probability, even for exponentially large samples. These linear inequalities can be selected in the...

real-valued function of n real variables. Linear equation over a ring Algebraic equation Line coordinates Linear inequality Nonlinear equation Barnett, Ziegler...

many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with...

specified by a linear inequality, derived from the linear equation that specifies the defining hyperplane. A strict linear inequality specifies an open...

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length...

mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph...

the Kantorovich inequality translates the basic idea of the triangle inequality into the terms and notational conventions of linear programming. (See...

In linear algebra, Weyl's inequality is a theorem about the changes to eigenvalues of an Hermitian matrix that is perturbed. It can be used to estimate...

thus related by the corresponding inequalities. Many inequalities satisfied by entropic vectors can be derived as linear combinations of a few basic ones...

facet-defining halfspaces. A closed half-space can be written as a linear inequality: a 1 x 1 + a 2 x 2 + ⋯ + a n x n ≤ b {\displaystyle a_{1}x_{1}+a_{2}x_{2}+\cdots...

inequality is a result that gives a lower bound for the bilinear form induced by a real linear elliptic partial differential operator. The inequality...

polyhedron defined by a single linear inequality, a1Tx ≤ b1. A hyperplane is a polyhedron defined by two inequalities, a1Tx ≤ b1 and a1Tx ≥ b1 (which...

mathematical inequalities. Agmon's inequality Askey–Gasper inequality Babenko–Beckner inequality Bernoulli's inequality Bernstein's inequality (mathematical...

of a linear code as an integer linear program, and then relax the integrality constraints on the variables into linear inequalities. "Using linear programming...

∈ Lp(μ) and g ∈ Lq(μ), then Hölder's inequality becomes an equality if and only if |f |p and |g|q are linearly dependent in L1(μ), meaning that there...

variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It...

homogeneous linear inequalities. Algebraically, each inequality is defined by a row of the matrix A {\displaystyle A} . Geometrically, each inequality defines...

n}} is a matrix. As with linear programs, ILPs not in standard form can be converted to standard form by eliminating inequalities, introducing slack variables...

In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral...

Trigonometric Functions Complex Numbers and Quadratic Equations Linear Inequalities Permutations and Combinations Binomial Theorem Sequences and Series...

of linear inequalities. It was originally proven by the Hungarian mathematician Gyula Farkas. Farkas' lemma is the key result underpinning the linear programming...

surjective linear maps B i : R n → R n i . {\displaystyle B_{i}:\mathbb {R} ^{n}\to \mathbb {R} ^{n_{i}}.} Then the following inequality holds: ∫ R n...

are linearly independent of each other and constrain the h-vectors (and therefore also the ƒ-vectors) in additional ways. Another important inequality on...