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  2. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere).

  3. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Generalized assignment problem; Integer programming. The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete [2] [3]: MP1 Some problems related to Job-shop scheduling; Knapsack problem, quadratic knapsack problem, and several variants [2] [3]: MP9

  4. Simplex algorithm - Wikipedia

    en.wikipedia.org/wiki/Simplex_algorithm

    In large linear-programming problems A is typically a sparse matrix and, when the resulting sparsity of B is exploited when maintaining its invertible representation, the revised simplex algorithm is much more efficient than the standard simplex method. Commercial simplex solvers are based on the revised simplex algorithm.

  5. P versus NP problem - Wikipedia

    en.wikipedia.org/wiki/P_versus_NP_problem

    An example is the simplex algorithm in linear programming, which works surprisingly well in practice; despite having exponential worst-case time complexity, it runs on par with the best known polynomial-time algorithms. [4]

  6. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    There is a close connection between linear programming problems, eigenequations, and von Neumann's general equilibrium model. The solution to a linear programming problem can be regarded as a generalized eigenvector. The eigenequations of a square matrix are as follows:

  7. Feasible region - Wikipedia

    en.wikipedia.org/wiki/Feasible_region

    A problem with five linear constraints (in blue, including the non-negativity constraints). In the absence of integer constraints the feasible set is the entire region bounded by blue, but with integer constraints it is the set of red dots. A closed feasible region of a linear programming problem with three variables is a convex polyhedron.