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  2. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    The proof establishes that, once the simplex algorithm finishes with a solution to the primal LP, it is possible to read from the final tableau, a solution to the dual LP. So, by running the simplex algorithm, we obtain solutions to both the primal and the dual simultaneously. [1]: 87–89 Another proof uses the Farkas lemma. [1]: 94

  3. HiGHS optimization solver - Wikipedia

    en.wikipedia.org/wiki/HiGHS_optimization_solver

    HiGHS has implementations of the primal and dual revised simplex method for solving LP problems, based on techniques described by Hall and McKinnon (2005), [6] and Huangfu and Hall (2015, 2018). [ 7 ] [ 8 ] These include the exploitation of hyper-sparsity when solving linear systems in the simplex implementations and, for the dual simplex ...

  4. Simplex algorithm - Wikipedia

    en.wikipedia.org/wiki/Simplex_algorithm

    The simplex method is remarkably efficient in practice and was a great improvement over earlier methods such as Fourier–Motzkin elimination. However, in 1972, Klee and Minty [32] gave an example, the Klee–Minty cube, showing that the worst-case complexity of simplex method as formulated by Dantzig is exponential time. Since then, for almost ...

  5. Duality (optimization) - Wikipedia

    en.wikipedia.org/wiki/Duality_(optimization)

    In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa).

  6. CPLEX - Wikipedia

    en.wikipedia.org/wiki/CPLEX

    The IBM ILOG CPLEX Optimizer solves integer programming problems, very large [3] linear programming problems using either primal or dual variants of the simplex method or the barrier interior point method, convex and non-convex quadratic programming problems, and convex quadratically constrained problems (solved via second-order cone programming, or SOCP).

  7. GLOP - Wikipedia

    en.wikipedia.org/wiki/GLOP

    GLOP (the Google Linear Optimization Package) is Google's open-source linear programming solver, created by Google's Operations Research Team.It is written in C++ and was released to the public as part of Google's OR-Tools software suite in 2014.

  8. Basic feasible solution - Wikipedia

    en.wikipedia.org/wiki/Basic_feasible_solution

    A basis B of the LP is called dual-optimal if the solution = is an optimal solution to the dual linear program, that is, it minimizes . In general, a primal-optimal basis is not necessarily dual-optimal, and a dual-optimal basis is not necessarily primal-optimal (in fact, the solution of a primal-optimal basis may even be unfeasible for the ...

  9. Big M method - Wikipedia

    en.wikipedia.org/wiki/Big_M_method

    Solve the problem using the usual simplex method. For example, x + y ≤ 100 becomes x + y + s 1 = 100, whilst x + y ≥ 100 becomes x + y − s 1 + a 1 = 100. The artificial variables must be shown to be 0. The function to be maximised is rewritten to include the sum of all the artificial variables.