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Convex Optimization Homework Solutions Form

Convex Optimization Homework Solutions Form

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we're going to sketch the proof of the following theorem if a linear programming problem has an optimal solution and this feasible region has an extreme point then it has an optimal solution that is an extreme point so this theorem confirms what you might have noticed already if you solve a linear programming problem graphically you often see Optimal Solutions that are Corners so let's get to the proof first of all we may assume without loss of generality that the linear programming problem is of the following form minimize C transpose X subject to A1 transpose X greater thanal to B1 up to a m transpose X greater than equal to BM where X is X1 up to xn so they are M constraints and N variables now typically linear programming problem might have less than or equal to constraint and equality constraints but less than equal to can be turned into a greater than equal to inequality just by multiplying both sides by minus one and if you have an equality you can write it as a

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