The simplex method, in mathematical optimization, is a well-known algorithm used for linear programming. As per the journal Computing in Science & Engineering, this method is considered one of the top 10 algorithms that originated during the twentieth century.
The simplex method presents an organized strategy for evaluating a feasible region's vertices. This helps to figure out the optimal value of the objective function.
George Dantzig developed the simplex method in 1946.
The method is also known as the simplex algorithm.
The simplex method is used to eradicate the issues in linear programming. It examines the feasible set's adjacent vertices in sequence to ensure that, at every new vertex, the objective function increases or is unaffected. In general, the simplex method is extremely powerful, which usually takes 2m to 3m iterations at the most (here, m denotes the range of equality constraints), and it converges in anticipated polynomial time for specific distributions of random input.
The simplex method uses a systematic strategy to generate and test candidate vertex solutions to a linear program. At every iteration, it chooses the variable that can make the biggest modification toward the minimum solution. That variable then replaces one of its covariables, which is most drastically limiting it, thereby shifting the simplex method to another part of the solution set and toward the final solution.
Furthermore, the simplex method is able to evaluate whether no solution actually exists. It can be observed that the algorithm is greedy as it opts for the best option at every iteration, with no demand for information from earlier or forthcoming iterations.
Sometimes, the principal data structure applied by the simplex method is referred to as a dictionary. Dictionaries include an illustration of the equations set that are properly fine tuned to the existing basis. Dictionaries can be used to offer an intuitive comprehension of why all variables enter and leave the basis.