Search results
Results from the WOW.Com Content Network
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]
The feasible set of the optimization problem consists of all points satisfying the inequality and the equality constraints. This set is convex because D {\displaystyle {\mathcal {D}}} is convex, the sublevel sets of convex functions are convex, affine sets are convex, and the intersection of convex sets is convex.
an infeasible problem is one for which no set of values for the choice variables satisfies all the constraints. That is, the constraints are mutually contradictory, and no solution exists; the feasible set is the empty set. unbounded problem is a feasible problem for which the objective function can be made to be better than any given finite ...
A basis of a greedoid is a maximal feasible set, meaning it is a feasible set but not contained in any other one. A basis of a subset X of E is a maximal feasible set contained in X. The rank of a greedoid is the size of a basis. By the exchange property, all bases have the same size. Thus, the rank function is well defined.
A. The feasible set {b+L} ∩ K is bounded, and intersects the interior of the cone K. B. We are given in advance a strictly-feasible solution x^, that is, a feasible solution in the interior of K. C. We know in advance the optimal objective value, c*, of the problem. D. We are given an M-logarithmically-homogeneous self-concordant barrier F ...
Typically, A is some subset of the Euclidean space, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. The domain A of f is called the search space or the choice set, while the elements of A are called candidate solutions or feasible solutions.
The following is the skeleton of a generic branch and bound algorithm for minimizing an arbitrary objective function f. [3] To obtain an actual algorithm from this, one requires a bounding function bound, that computes lower bounds of f on nodes of the search tree, as well as a problem-specific branching rule.
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.