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  2. 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 ...

  3. Constrained optimization - Wikipedia

    en.wikipedia.org/wiki/Constrained_optimization

    If the constrained problem has only equality constraints, the method of Lagrange multipliers can be used to convert it into an unconstrained problem whose number of variables is the original number of variables plus the original number of equality constraints. Alternatively, if the constraints are all equality constraints and are all linear ...

  4. Karush–Kuhn–Tucker conditions - Wikipedia

    en.wikipedia.org/wiki/Karush–Kuhn–Tucker...

    The system of equations and inequalities corresponding to the KKT conditions is usually not solved directly, except in the few special cases where a closed-form solution can be derived analytically. In general, many optimization algorithms can be interpreted as methods for numerically solving the KKT system of equations and inequalities. [7]

  5. List of optimization software - Wikipedia

    en.wikipedia.org/wiki/List_of_optimization_software

    In continuous optimization, A is some subset of the Euclidean space R n, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. In combinatorial optimization, A is some subset of a discrete space, like binary strings, permutations, or sets of integers.

  6. Slack variable - Wikipedia

    en.wikipedia.org/wiki/Slack_variable

    In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality constraint. A non-negativity constraint on the slack variable is also added. [1]: 131 Slack variables are used in particular in linear programming.

  7. Big M method - Wikipedia

    en.wikipedia.org/wiki/Big_M_method

    The Big M method introduces surplus and artificial variables to convert all inequalities into that form. The "Big M" refers to a large number associated with the artificial variables, represented by the letter M. The steps in the algorithm are as follows: Multiply the inequality constraints to ensure that the right hand side is positive.

  8. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1] It is named after the mathematician Joseph-Louis ...

  9. Convex optimization - Wikipedia

    en.wikipedia.org/wiki/Convex_optimization

    The feasible set of the optimization problem consists of all points satisfying the inequality and the equality constraints. This set is convex because D {\displaystyle {\mathcal {D}}} is convex, the sublevel sets of convex functions are convex, affine sets are convex, and the intersection of convex sets is convex.