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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. 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.

  4. Taylor's theorem - Wikipedia

    en.wikipedia.org/wiki/Taylor's_theorem

    v. t. e. In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function.

  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. Linear equation - Wikipedia

    en.wikipedia.org/wiki/Linear_equation

    Conversely, every line is the set of all solutions of a linear equation. The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding ...

  7. Poincaré inequality - Wikipedia

    en.wikipedia.org/wiki/Poincaré_inequality

    Poincaré inequality. In mathematics, the Poincaré inequality[1] is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition. Such bounds are of great importance in the ...

  8. Jensen's inequality - Wikipedia

    en.wikipedia.org/wiki/Jensen's_inequality

    Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. 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 of the convex function. It was proved by Jensen in 1906, [1] building on an ...

  9. Simplex algorithm - Wikipedia

    en.wikipedia.org/wiki/Simplex_algorithm

    A system of linear inequalities defines a polytope as a feasible region. The simplex algorithm begins at a starting vertex and moves along the edges of the polytope until it reaches the vertex of the optimal solution. Polyhedron of simplex algorithm in 3D. The simplex algorithm operates on linear programs in the canonical form.

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