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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.
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.
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 ...
The problem is to rapidly find a solution among candidates a, b, and c that is as good as any other, where goodness is either 0 or 1. There are eight instances ("lunch plates") fxyz of the problem, where x, y, and z indicate the goodness of a, b, and c, respectively. Procedure ("restaurant") A evaluates candidates in the order a, b, c, and B ...
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables , which is solved by constraint satisfaction methods.
A constraint optimization problem (COP) is a constraint satisfaction problem associated to an objective function. An optimal solution to a minimization (maximization) COP is a solution that minimizes (maximizes) the value of the objective function. During the search of the solutions of a COP, a user can wish for:
By using the dual form of this constraint optimization problem, it can be used to calculate the gradient very fast. A nice property is that the number of computations is independent of the number of parameters for which you want the gradient. The adjoint method is derived from the dual problem [4] and is used e.g. in the Landweber iteration ...
Constrained conditional models form a learning and inference framework that augments the learning of conditional (probabilistic or discriminative) models with declarative constraints (written, for example, using a first-order representation) as a way to support decisions in an expressive output space while maintaining modularity and ...