Transcription of Chapter 4 Duality - Stanford University
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Chapter 4 Duality - Stanford University
Chapter 4 DualityGiven any linear program, there is another related linear program called thedual. In this Chapter , we will develop an understanding of the dual linearprogram. This understanding translates to important insights about manyoptimization problems and algorithms. We begin in the next section byexploring the main concepts of Duality through the simple graphical exampleof building cars and trucks that was introduced in Section Then, wewill develop the theory of Duality in greater generality and explore moresophisticated A Graphical ExampleRecall the linear program from Section , which determines the optimalnumbers of cars and trucks to build in light of capacity constraints. There aretwo decision variables: the number of carsx1in thousands and the numberof trucksx2in thousands.
c Benjamin Van Roy and Kahn Mason 85 Note that the matrix A has full rank. Therefore, it has an inverse A−1. Through some calculations, we get (approximately) A−1 = " 0.389 −0.185 −0.195 0.259 #. The optimal solution of the linear program is given by x = A−1b, and there-fore, the optimal profit is cTA−1b = 77.3. 4.1.1 Sensitivity ...
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