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  2. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    Solve example Linear Programming (LP) problems through MATLAB, Python, or a web-interface. CPLEX Popular solver with an API for several programming languages, and also has a modelling language and works with AIMMS, AMPL, GAMS , MPL, OpenOpt, OPL Development Studio, and TOMLAB .

  3. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    Suppose we have the linear program: Maximize c T x subject to Ax ≤ b, x ≥ 0.. We would like to construct an upper bound on the solution. So we create a linear combination of the constraints, with positive coefficients, such that the coefficients of x in the constraints are at least c T.

  4. Linear programming relaxation - Wikipedia

    en.wikipedia.org/wiki/Linear_programming_relaxation

    The linear programming relaxation of an integer program may be solved using any standard linear programming technique. If it happens that, in the optimal solution, all variables have integer values, then it will also be an optimal solution to the original integer program.

  5. HiGHS optimization solver - Wikipedia

    en.wikipedia.org/wiki/HiGHS_optimization_solver

    HiGHS has an interior point method implementation for solving LP problems, based on techniques described by Schork and Gondzio (2020). [10] It is notable for solving the Newton system iteratively by a preconditioned conjugate gradient method, rather than directly, via an LDL* decomposition. The interior point solver's performance relative to ...

  6. lp_solve - Wikipedia

    en.wikipedia.org/wiki/Lp_solve

    lp_solve is a free software command line utility and library for solving linear programming and mixed integer programming problems. It ships with support for two file formats, MPS and lp_solve's own LP format. [ 1 ]

  7. Interior-point method - Wikipedia

    en.wikipedia.org/wiki/Interior-point_method

    An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967. [1] The method was reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, [2] which runs in provably polynomial time (() operations on L-bit numbers, where n is the number of variables and constants), and is also very ...

  8. Karmarkar's algorithm - Wikipedia

    en.wikipedia.org/wiki/Karmarkar's_algorithm

    Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice.

  9. Basic feasible solution - Wikipedia

    en.wikipedia.org/wiki/Basic_feasible_solution

    For the definitions below, we first present the linear program in the so-called equational form: . maximize subject to = and . where: and are vectors of size n (the number of variables);