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2. Linear inequality - Wikipedia

   en.wikipedia.org/wiki/Linear_inequality

   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.

3. Farkas' lemma - Wikipedia

   en.wikipedia.org/wiki/Farkas'_lemma

   In mathematics, Farkas' lemma is a solvability theorem for a finite system of linear inequalities. It was originally proven by the Hungarian mathematician Gyula Farkas. [1] Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization (alternatively ...

4. Inequality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Inequality_(mathematics)

   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.

5. Linear programming - Wikipedia

   en.wikipedia.org/wiki/Linear_programming

   Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the ...

6. Cutting-plane method - Wikipedia

   en.wikipedia.org/wiki/Cutting-plane_method

   In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general ...

7. Relaxation (iterative method) - Wikipedia

   en.wikipedia.org/wiki/Relaxation_(iterative_method)

   Relaxation (iterative method) In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems. [1] Relaxation methods were developed for solving large sparse linear systems, which arose as finite-difference discretizations of differential equations. [2][3] They are also used for ...