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...

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

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

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...

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

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 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...

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...

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

∈ 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...

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

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

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...

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

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...

Fujishige, Satoru (1984), "A System of Linear inequalities with a Submodular Function on (0, ±1) Vectors", Linear Algebra and Its Applications, 63: 253–266...

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

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

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

related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector...

from the immediately preceding layer Linear programming – maximize a linear function subject to linear inequality constraints Lexicographically first depth...

Optimization (PDF), Wiley. Agmon, Shmuel (1954), "The relaxation method for linear inequalities", Canadian Journal of Mathematics, 6: 382–392, doi:10.4153/CJM-1954-037-2...