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  2. Feasible region - Wikipedia

    en.wikipedia.org/wiki/Feasible_region

    In mathematical optimization and computer science, a feasible region, feasible set, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. [1]

  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. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real -valued affine (linear) function defined on this polytope.

  5. Cutting-plane method - Wikipedia

    en.wikipedia.org/wiki/Cutting-plane_method

    If it is not, there is guaranteed to exist a linear inequality that separates the optimum from the convex hull of the true feasible set. Finding such an inequality is the separation problem, and such an inequality is a cut. A cut can be added to the relaxed linear program. Then, the current non-integer solution is no longer feasible to the ...

  6. Interior-point method - Wikipedia

    en.wikipedia.org/wiki/Interior-point_method

    To initialize the path-following methods, we need a point in the relative interior of the feasible region G. In other words: if G is defined by the inequalities g i (x) ≤ 0, then we need some x for which g i (x) < 0 for all i in 1,...,m. If we do not have such a point, we need to find one using a so-called phase I method.

  7. 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

  8. Inequation - Wikipedia

    en.wikipedia.org/wiki/Inequation

    Solution set (portrayed as feasible region) for a sample list of inequations. Similar to equation solving, inequation solving means finding what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an inequation or a conjunction of several inequations.

  9. Barrier function - Wikipedia

    en.wikipedia.org/wiki/Barrier_function

    [1] [2] Such functions are used to replace inequality constraints by a penalizing term in the objective function that is easier to handle. A barrier function is also called an interior penalty function, as it is a penalty function that forces the solution to remain within the interior of the feasible region.