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Unformatted text preview: f , we can consider the following linear program: min u = f s.t. x 1 + x 2 ≥ 4 2 x 1 + x 2 ≤ 5 3 x 1 + 4 x 2 ≤ f 5 x 1 + 2 x 2 ≤ f If ( x * 1 ,x * 2 ,f * ) is an optimal solution of the linear program, then ( x * 1 ,x * 2 ) is an optimal solution of the minimax problem, and f * is the optimal value of the minimax problem. Also, we have f * = max { 3 x * 1 + 4 x * 2 , 5 x * 1 + 2 x * 2 } . All minimax problems can be converted to linear programs, it is similar for maximin problems. 19 Handling absolute values: another way ● Observe that z = max {z, – z} ● So the problem min x 1 – x 2  s.t. x 1 + x 2 ≥ 4 becomes min max {x 1 – x 2 , x 2 – x 1 } s.t. x 1 + x 2 ≥ 4 ● Now it can be handled as a minimax program ● This works when the original problem is a minimization...
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 Spring '08
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 Operations Research, Optimization, linear program, Minimax, ) Objective Functions

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