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...

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

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

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...

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...

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...

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

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

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

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

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...

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

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

Zhang-Yeung inequality. Matus proved that no finite set of inequalities can characterize (by linear combinations) all entropic inequalities. In other words...

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

In physics and mathematics, the Golden–Thompson inequality is a trace inequality between exponentials of symmetric and Hermitian matrices proved independently...

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...

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

for linear inequalities and linear programs (especially 16.2 Relaxation methods, and 16.4 Sparsity-preserving iterative SOR algorithms for linear programming)"...

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

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...

∈ 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...