homework2 - EGM6365 Homework#2 1 Consider the following...

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EGM6365 Homework #2 1. Consider the following design optimization problem: 22 12 1 11 3 32 1 Minimize ( ) 4 4 Subject to ( ) 0 () 0 ( 1 ) 0 fx x x gx x =+− + =− ≤ =− =−− ≤ x x x x (i) Find the optimum point graphically (ii) Show that the optimum point does not satisfy K-T condition. Explain 2. An engineering design problem is formulated as: Minimize 121 2 2 5 2 1 0 x x x =+ − − + x Subject to the constraints 2 112 23 0 326 0 hx x gxx =+ −= =+ In all of the following questions, justify your answers. (i) Write K-T necessary conditions (ii) How many cases are there to be considered? Identify those cases. (iii) Find the solution for the case where g 1 is active. Is this acceptable case? (iv) Regardless of the solution you obtained in (iii), suppose the Lagrange multiplier for the constraint h 1 = 0 is λ 1 = -2 and the Lagrange multiplier for the constraint
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