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R(k,:)=M(k,:)-M(k,j_in)*R(l_out,:) % Set them equal to the original matrix Minus a multiple of normalized row l_out, making R(k,j_in)=0
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R(l_out,:)=M(l_out,:)/M(l_out,j_in) % Copy row l_out, normalizing M(l_out,j_in) to 1 % formed into a unit vector with u(l_out) = 1 and u(i) = 0 for % operations on (pivot row index is l_out). % Compute the new inverse basis B^-1 by performing elementary row % Value of the entering variable is theta L = find(x(C)./u = theta) % Find all indices with ratio theta % 'return' to break from the function, e.g.į_opt = -inf % Optimal objective function cost = -inf % Compute the vector of reduced costs c_rĬ_r = c' - p'*A % Vector of reduced costs % compute the inital basic feasible solution % Create the initial Basis matrix, compute its inverse and % Initialize the vector of decision variables % NOTE: Replace 12345X with your own student numberįunction = SXXXXX(A,b,c,C) % f_opt: Objective function value at the optimal solution % x_opt: Decision variable values at the optimal solution % C: The indices of the basic variables corresponding to an % The function input parameters are the following: Here's the code I wrote: %% Implementation of the revised Simplex. The vector u is transformed into a unit vector with u(l_out) = 1 and u(i) = 0 for other i. The problem is only related to a part of the code, the one in the bottom of the script aiming at:Ĭomputing the new inverse basis B^-1 by performing elementary row operations on (pivot row index is l_out). The code I wrote runs without problems with input data although I've realised it doesn't solve the problem properly, as it does not update the inverse of the basis B (the real core idea of the abovementioned method). I've been asked to write down a Matlab program in order to solve LPs using the Revised Simplex Method.
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