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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.
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).
In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron P {\displaystyle P} and a vector x ∗ ∈ R n {\displaystyle \mathbf {x} ^{*}\in \mathbb {R} ^{n}} , x ∗ {\displaystyle \mathbf {x} ^{*}} is a ...
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.
where x i is a basic variable and the x j 's are the nonbasic variables (i.e. the basic solution which is an optimal solution to the relaxed linear program is = ¯ and =). We write coefficients b ¯ i {\displaystyle {\bar {b}}_{i}} and a ¯ i , j {\displaystyle {\bar {a}}_{i,j}} with a bar to denote the last tableau produced by the simplex method.
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.
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 ...
Feasible region, a region that satisfies mathematical constraints; Logical possibility, an achievable thing; See also. Pragmatism This page was last edited on 17 ...