toetusvektoritest

Toetusvektoritest is a mathematical method used to determine the feasibility and optimality of a solution in linear programming problems. It is a systematic approach to verify whether a given point (often referred to as a candidate solution) is a basic feasible solution and, if so, whether it is optimal.

The test involves examining the coefficients of the objective function and the constraints to determine the nature of the solution. Specifically, it checks whether the solution is non-degenerate, meaning that the number of basic variables equals the number of constraints. If the solution is non-degenerate, the test proceeds by evaluating the reduced costs associated with the non-basic variables. If all reduced costs are non-negative, the solution is optimal. If any reduced costs are negative, the solution is not optimal, and the problem can be improved by adjusting the values of the basic variables.

The toetusvektoritest is a crucial tool in the simplex method, a popular algorithm for solving linear programming problems. It helps in identifying the direction in which the objective function can be improved and guides the algorithm towards the optimal solution. By systematically applying the toetusvektoritest, one can ensure that the solution obtained is indeed the best possible within the given constraints.