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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

    The constrained-optimization problem (COP) is a significant generalization of the classic constraint-satisfaction problem (CSP) model. [1] COP is a CSP that includes an objective function to be optimized. Many algorithms are used to handle the optimization part.

  4. 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.

  5. Mathematical optimization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_optimization

    It studies the case in which the optimization strategy is based on splitting the problem into smaller subproblems. The equation that describes the relationship between these subproblems is called the Bellman equation. Mathematical programming with equilibrium constraints is where the constraints include variational inequalities or ...

  6. 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]

  7. Big M method - Wikipedia

    en.wikipedia.org/wiki/Big_M_method

    However, to apply it, the origin (all variables equal to 0) must be a feasible point. This condition is satisfied only when all the constraints (except non-negativity) are less-than constraints and with positive constant on the right-hand side. The Big M method introduces surplus and artificial variables to convert all inequalities into that form.

  8. Ellipsoid method - Wikipedia

    en.wikipedia.org/wiki/Ellipsoid_method

    Then we proceed to the next inequality constraint. For each constraint, we either convert it to equality or remove it. Finally, we have only equality constraints, which can be solved by any method for solving a system of linear equations. Step 3: the decision problem can be reduced to a different optimization problem.

  9. Optimization problem - Wikipedia

    en.wikipedia.org/wiki/Optimization_problem

    g i (x) ≤ 0 are called inequality constraints; h j (x) = 0 are called equality constraints, and; m ≥ 0 and p ≥ 0. If m = p = 0, the problem is an unconstrained optimization problem. By convention, the standard form defines a minimization problem.