Search results
Results from the WOW.Com Content Network
In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds to a vertex of the polyhedron of feasible solutions.
A constraint is active for a particular solution if it is satisfied at equality for that solution. A basic solution that satisfies all the constraints defining P {\displaystyle P} (or, in other words, one that lies within P {\displaystyle P} ) is called a basic feasible solution .
The possible results of Phase I are either that a basic feasible solution is found or that the feasible region is empty. In the latter case the linear program is called infeasible. In the second step, Phase II, the simplex algorithm is applied using the basic feasible solution found in Phase I as a starting point.
However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere).
The method proceeds by first dropping the requirement that the x i be integers and solving the associated relaxed linear programming problem to obtain a basic feasible solution. Geometrically, this solution will be a vertex of the convex polytope consisting of all feasible points.
The space of all candidate solutions, before any feasible points have been excluded, is called the feasible region, feasible set, search space, or solution space. [2] This is the set of all possible solutions that satisfy the problem's constraints. Constraint satisfaction is the process of finding a point in the feasible set.
Finding a solution to ensure the program’s long-term solvency is critical for the estimated 67 million Americans who rely on Social Security — and for future generations. 5 proposed solutions ...
The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.