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optimization - All optimal solutions of a linear program - Mathematics . . . If this GAMS program terminates normally, i e no execution or compilation error, the exploration for alternative solutions proceeds " - GAMS You can also enumerate all solutions as explained here If it's a MIP problem, Gurobi can attempt to find multiple optimal solutions
optimization - Set of optimal solutions for a linear programs . . . $\begingroup$ I have problems to say optimal solutions In the question it is stated, that the set is unbounded Thus there is no optimal solution like a specific combination or a line You can name some solutions by calculating feasible solutions For example (x_1,x2)=(100,49) holds for both restrictions
Multiple optimal solutions LP - Mathematics Stack Exchange Therefore, the only way to determine whether there is an alternate basic optimal feasible solution from the optimal simplex tableau is to search for the zeros in the reduced cost coefficient of the non-basic variables
LP: multiple optimal solutions, unbounded, infeasible? $\begingroup$ My idea is that Minimize z = y -3x has multiple solutions because it runs parallel to one of the constraints, but are these solutions optimal (how do I find this in general?) For (2) I read that an LP with a bounded feasible region always has a finite optimal solution, but I can't change the feasible region can I?
Can a non-degenerate LP have multiple optimal solutions? In linear programming, an LP can have multiple optimal solutions if it contains degenerate vertices, i e where one of the base-variables is 0 Can an LP also have multiple optimal solutions if it does not contain degenerate solutions? If so, what is an example LP?
linear programming - Find all optimal solutions by Simplex . . . It's easy to verify that any convex combination of a set of basic optimal feasible solution(s) is still an optimal feasible solution (since the feasible region in a linear program in convex), so the set of optimal feasible solution is convex (i e path connected) Hence, the answer to your question is yes
Duality Theorem - Optimal solution of both Primal and Dual The Duality Theorem, in short, states that the optimal value of the Primal (P) and Dual (D) Linear Programs are the same if the solution, of either, is a basic feasible solution My question is that it also follows that (from Linear and Nonlinear Programming - Luenberger, Ye), from a corollary to the Weak Duality Lemma