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  2. Nelder–Mead method - Wikipedia

    en.wikipedia.org/wiki/Nelder–Mead_method

    Simplex vertices are ordered by their value, with 1 having the lowest (best) value. The Nelder–Mead method (also downhill simplex method, amoeba method, or polytope method) is a numerical method used to find the minimum or maximum of an objective function in a multidimensional space.

  3. 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 ...

  4. 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.

  5. Mathematical optimization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_optimization

    Conditional gradient method (Frank–Wolfe) for approximate minimization of specially structured problems with linear constraints, especially with traffic networks. For general unconstrained problems, this method reduces to the gradient method, which is regarded as obsolete (for almost all problems).

  6. Bland's rule - Wikipedia

    en.wikipedia.org/wiki/Bland's_rule

    With Bland's rule, the simplex algorithm solves feasible linear optimization problems without cycling. [1] [2] [3] The original simplex algorithm starts with an arbitrary basic feasible solution, and then changes the basis in order to decrease the minimization target and find an optimal solution. Usually, the target indeed decreases in every ...

  7. Least absolute deviations - Wikipedia

    en.wikipedia.org/wiki/Least_absolute_deviations

    A Simplex method is a method for solving a problem in linear programming. The most popular algorithm is the Barrodale-Roberts modified Simplex algorithm. The algorithms for IRLS, Wesolowsky's Method, and Li's Method can be found in Appendix A of [7] among other methods. Checking all combinations of lines traversing any two (x,y) data points is ...

  8. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    In 1947, Dantzig also invented the simplex method that, for the first time efficiently, tackled the linear programming problem in most cases. [8] When Dantzig arranged a meeting with John von Neumann to discuss his simplex method, von Neumann immediately conjectured the theory of duality by realizing that the problem he had been working in game ...

  9. Klee–Minty cube - Wikipedia

    en.wikipedia.org/wiki/Klee–Minty_cube

    Klee Minty cube for shadow vertex simplex method. The Klee–Minty cube or Klee–Minty polytope (named after Victor Klee and George J. Minty) is a unit hypercube of variable dimension whose corners have been perturbed.