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  2. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function or Lagrangian. [2]

  3. 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 ...

  4. Feasible region - Wikipedia

    en.wikipedia.org/wiki/Feasible_region

    In contrast, the feasible set formed by the constraint set {x ≥ 0, y ≥ 0, x + 2y ≤ 4} is bounded because the extent of movement in any direction is limited by the constraints. In linear programming problems with n variables, a necessary but insufficient condition for the feasible set to be bounded is that the number of constraints be at ...

  5. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    lp solve: LGPL v2.1: An LP and MIP solver featuring support for the MPS format and its own "lp" format, as well as custom formats through its "eXternal Language Interface" (XLI). [30] [31] Translating between model formats is also possible. [32] Qoca: GPL: A library for incrementally solving systems of linear equations with various goal ...

  6. Augmented Lagrangian method - Wikipedia

    en.wikipedia.org/wiki/Augmented_Lagrangian_method

    Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective, but the augmented Lagrangian method adds yet another term designed to mimic a Lagrange multiplier.

  7. Linear programming relaxation - Wikipedia

    en.wikipedia.org/wiki/Linear_programming_relaxation

    In a maximization problem the fraction is reversed. The integrality gap is always at least 1. In the example above, the instance F = {{a, b}, {b, c}, {a, c}} shows an integrality gap of 4/3. Typically, the integrality gap translates into the approximation ratio of an approximation algorithm.

  8. USA falls to Finland: World juniors hockey 2025 schedule, how ...

    www.aol.com/usa-looks-defend-world-juniors...

    Dec. 28: United States 5, Latvia 1. Danny Nelson scored two goals, including 1:58 into the first period. The USA got goals from Ryan Leonard, Zeev Buium and Nelson in the second period to pull away.

  9. Assignment problem - Wikipedia

    en.wikipedia.org/wiki/Assignment_problem

    Some of the local methods assume that the graph admits a perfect matching; if this is not the case, then some of these methods might run forever. [1]: 3 A simple technical way to solve this problem is to extend the input graph to a complete bipartite graph, by adding artificial edges with very large weights. These weights should exceed the ...

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