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  2. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

  3. Assignment problem - Wikipedia

    en.wikipedia.org/wiki/Assignment_problem

    The formal definition of the assignment problem (or linear assignment problem) is . Given two sets, A and T, together with a weight function C : A × T → R.Find a bijection f : A → T such that the cost function:

  4. Design optimization - Wikipedia

    en.wikipedia.org/wiki/Design_optimization

    Design optimization applies the methods of mathematical optimization to design problem formulations and it is sometimes used interchangeably with the term engineering optimization. When the objective function f is a vector rather than a scalar, the problem becomes a multi-objective optimization one.

  5. Dynamic programming - Wikipedia

    en.wikipedia.org/wiki/Dynamic_programming

    This usage is the same as that in the phrases linear programming and mathematical programming, a synonym for mathematical optimization. [ 18 ] The above explanation of the origin of the term may be inaccurate: According to Russell and Norvig, the above story "cannot be strictly true, because his first paper using the term (Bellman, 1952 ...

  6. 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 ...

  7. Linear-fractional programming - Wikipedia

    en.wikipedia.org/wiki/Linear-fractional_programming

    In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear ...

  8. Levenberg–Marquardt algorithm - Wikipedia

    en.wikipedia.org/wiki/Levenberg–Marquardt...

    The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters ⁠ ⁠ of the model curve (,) so that the sum of the squares of the deviations () is minimized:

  9. Branch and cut - Wikipedia

    en.wikipedia.org/wiki/Branch_and_cut

    This description assumes the ILP is a maximization problem.. The method solves the linear program without the integer constraint using the regular simplex algorithm.When an optimal solution is obtained, and this solution has a non-integer value for a variable that is supposed to be integer, a cutting plane algorithm may be used to find further linear constraints which are satisfied by all ...