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The second and third lines define two constraints, the first of which is an inequality constraint and the second of which is an equality constraint. These two constraints are hard constraints, meaning that it is required that they be satisfied; they define the feasible set of candidate solutions. Without the constraints, the solution would be ...
One way for evaluating this upper bound for a partial solution is to consider each soft constraint separately. For each soft constraint, the maximal possible value for any assignment to the unassigned variables is assumed. The sum of these values is an upper bound because the soft constraints cannot assume a higher value.
The composition of such two constraints is the constraint ((,),) that is satisfied by every evaluation of the two non-shared variables for which there exists a value of the shared variable such that the evaluation of these three variables satisfies the two original constraints ((,),) and ((,),).
Problems in rigid body dynamics (in particular articulated rigid body dynamics) often require mathematical programming techniques, since you can view rigid body dynamics as attempting to solve an ordinary differential equation on a constraint manifold; [11] the constraints are various nonlinear geometric constraints such as "these two points ...
To see this, note that the two constraints x 1 (x 1 − 1) ≤ 0 and x 1 (x 1 − 1) ≥ 0 are equivalent to the constraint x 1 (x 1 − 1) = 0, which is in turn equivalent to the constraint x 1 ∈ {0, 1}. Hence, any 0–1 integer program (in which all variables have to be either 0 or 1) can be formulated as a quadratically constrained ...
In relational database theory, a functional dependency is the following constraint between two attribute sets in a relation: Given a relation R and attribute sets ,, X is said to functionally determine Y (written X → Y) if each X value is associated with precisely one Y value.
A binary constraint, in mathematical optimization, is a constraint that involves exactly two variables. For example, consider the n-queens problem, where the goal is to place n chess queens on an n-by-n chessboard such that none of the queens can attack each other (horizontally, vertically, or diagonally). The formal set of constraints are ...
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.