Search results
Results From The WOW.Com Content Network
A LP can also be unbounded or infeasible. Duality theory tells us that: If the primal is unbounded, then the dual is infeasible; If the dual is unbounded, then the primal is infeasible. However, it is possible for both the dual and the primal to be infeasible. Here is an example:
A closed feasible region of a linear programming problem with three variables is a convex polyhedron. 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 ...
A closed feasible region of a problem with three variables is a convex polyhedron. The surfaces giving a fixed value of the objective function are planes (not shown). The linear programming problem is to find a point on the polyhedron that is on the plane with the highest possible value.
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.
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.
An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967. [1] The method was reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, [2] which runs in provably polynomial time (() operations on L-bit numbers, where n is the number of variables and constants), and is also very ...
An infeasible value of the candidate solution is one that exceeds one or more of the constraints. In the dual problem, the dual vector multiplies the constraints that determine the positions of the constraints in the primal. Varying the dual vector in the dual problem is equivalent to revising the upper bounds in the primal problem.
In mathematical optimization, the fundamental theorem of linear programming states, in a weak formulation, that the maxima and minima of a linear function over a convex polygonal region occur at the region's corners.