Therefore, in MATLAB syntax, each variable becomes: f = With respect to the linear programming formulation, we can now see what each variable in the MATLAB universe needs to be. If we reformulate your problem into matrix form for the above, we now get: x would be the solution to the linear programming problem formulated. linprog accepts syntax in the following way: x = linprog(f,A,b,Aeq,beq) į is a vector of coefficients that work with the objective function, A is a matrix of coefficients that work with the inequality, b is a vector of coefficients that are for the right-hand side of each inequality constraint, and Aeq, beq, are the same as the inequality but for the equality constraints. All you have to do now is plug this problem into linprog. Note that we don't have any upper or lower bounds as those conditions are already satisfied in the equality and inequality constraints. Therefore, with the above, your formulation is now: In addition, MATLAB doesn't support strict inequalities, and so what you'll have to do is enforce a constraint so that you are checking to see if each variable is lesser than a small number, perhaps something like setting a threshold epsilon to 1e-4. Because you want to find the minimum possible value that satisfies the above constraint given, what you're really after is:īecause MATLAB only supports inequalities of less than, you'll need to take the negative of the first two constraints. You seek to find a solution x in R^n which minimizes the objective function f^*x subject to a set of inequality constraints, equality constraints, and each component in x is bounded between a lower and upper bound. A linear program in the MATLAB universe can be formulated like so: Building on what jlandercy said, you can certainly use MATLAB's linprog function, which is MATLAB's linear programming solver.
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