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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. Chance constrained programming - Wikipedia

    en.wikipedia.org/wiki/Chance_constrained_programming

    A general chance constrained optimization problem can be formulated as follows: (,,) (,,) =, {(,,)}Here, is the objective function, represents the equality constraints, represents the inequality constraints, represents the state variables, represents the control variables, represents the uncertain parameters, and is the confidence level.

  4. Optimization problem - Wikipedia

    en.wikipedia.org/wiki/Optimization_problem

    Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.

  5. Karush–Kuhn–Tucker conditions - Wikipedia

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

    Consider the following nonlinear optimization problem in standard form: . minimize () subject to (),() =where is the optimization variable chosen from a convex subset of , is the objective or utility function, (=, …,) are the inequality constraint functions and (=, …,) are the equality constraint functions.

  6. Constraint satisfaction problem - Wikipedia

    en.wikipedia.org/.../Constraint_satisfaction_problem

    The classic model of Constraint Satisfaction Problem defines a model of static, inflexible constraints. This rigid model is a shortcoming that makes it difficult to represent problems easily. [ 33 ] Several modifications of the basic CSP definition have been proposed to adapt the model to a wide variety of problems.

  7. Scenario optimization - Wikipedia

    en.wikipedia.org/wiki/Scenario_optimization

    In optimization, robustness features translate into constraints that are parameterized by the uncertain elements of the problem. In the scenario method, [ 1 ] [ 2 ] [ 3 ] a solution is obtained by only looking at a random sample of constraints ( heuristic approach) called scenarios and a deeply-grounded theory tells the user how “robust ...

  8. Constraint (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Constraint_(mathematics)

    In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set. [1]

  9. Active-set method - Wikipedia

    en.wikipedia.org/wiki/Active-set_method

    In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem.