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  2. 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.

  3. 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]

  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. Big M method - Wikipedia

    en.wikipedia.org/wiki/Big_M_method

    For less-than or equal constraints, introduce slack variables s i so that all constraints are equalities. 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.

  7. 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.

  8. 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.

  9. Feasible region - Wikipedia

    en.wikipedia.org/wiki/Feasible_region

    In mathematical optimization and computer science, a feasible region, feasible set, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. [1]