# HW4 - EAS6939 Homework#4(Due 3/22 1 Consider the following...

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EAS6939 Homework #4 (Due: 3/22) 1. Consider the following design optimization problem: 22 1 2 1 11 3 3 2 1 Minimize ( ) 4 4 Subject to ( ) 0 ( ) 0 ( ) (1 ) 0 f x x x gx g x 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 1 2 1 2 ( ) 2 5 2 10 f x x x x x Subject to the constraints 1 1 2 1 1 2 2 3 0 3 2 6 0 h x x g x x     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 1 = -2 and the Lagrange multiplier for the constraint
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## This note was uploaded on 02/15/2012 for the course EAS 6939 taught by Professor Staff during the Spring '08 term at University of Florida.

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