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A linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign. Two-dimensional linear inequalities are...

linear inequalities implies (for feasible problems) that for every vertex x* of the LP feasible region, there exists a set of d (or fewer) inequality...

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...

widely used inequalities in mathematics. The inequality for sums was published by Augustin-Louis Cauchy (1821). The corresponding inequality for integrals...

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

variables are eliminated from a system of linear inequalities, then one obtains a system of constant inequalities. It is then trivial to decide whether the...

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

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

strict inequalities, meaning that a is strictly less than or strictly greater than b. Equality is excluded. In contrast to strict inequalities, there...

the boundedness of an iterative procedure for solving a system of linear inequalities". Proceedings of the American Mathematical Society. 26 (2): 229–235...

Friedrichs's inequality Gagliardo–Nirenberg interpolation inequality Gårding's inequality Grothendieck inequality Grunsky's inequalities Hanner's inequalities Hardy's...

quadratic inequalities is undecidable. Ray tracing in 3-D optical systems with a finite set of refractive objects represented by a system of rational linear inequalities...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

{\displaystyle b_{m}} of the scalar inequalities. An open convex polytope is defined in the same way, with strict inequalities used in the formulas instead of...

Motzkin, T. S.; Schoenberg, I. J. (1954), "The relaxation method for linear inequalities", Canadian Journal of Mathematics, 6: 393–404, doi:10.4153/CJM-1954-038-x...

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

of linear programming and related problems in mathematical optimization, convex polytopes are often described by a system of linear inequalities that...

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, a linear equation is an equation that may be put in the form a 1 x 1 + … + a n x n + b = 0 , {\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0...

In mathematics, the Brascamp–Lieb inequality is either of two inequalities. The first is a result in geometry concerning integrable functions on n-dimensional...