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HW6 - MS&E 211 Linear& Nonlinear Optimization Fall...

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Unformatted text preview: MS&E 211 Linear & Nonlinear Optimization Fall 2011 Prof Yinyu Ye Homework Assignment 6: Due Tuesday December 6 th at 6:00pm 1. Log-Barrier Method: [25points] (a) [10points] Solve using the log-barrier method: gG¡G¢G£¤: ¥ ¦ § + 3¥ ¦ ¥ § + ¥ § § ¨©ª«¤¬­ ­®: ¥ ¦ + ¥ § = 1 ¥ ¦ , ¥ § ≥ 0 (b) [10points] Solve using the log-barrier method: gG¡G¢G£¤: 1 2 ¯ ¦ § + 1 2 ¯ § § − ¯ ¦ − 2¯ § ¨©ª«¤¬­ ­®: ¯ ¦ + ¯ § ≥ 4 (c) [5points] Explain why we can or cannot guarantee convergence to the optimal solution in part b. 2. Central Path of a linear program [20points] Consider the linear program: gG¡G¢G£¤: ¯ ¦ + ¯ § °©ª«¤¬­ ­®: ¯ ¦ + ¯ § + ¯ ± = 1 ¯ ¦ , ¯ § ,¯ ± ≥ 0 (a) [10points] Formulate the barriered problem using a logarithmic barrier and derive the KKT optimality condition for the barriered problem. Resolve the optimal solution in terms of the barrier parameter ²: ¯ ¦ ∗ ³²´, ¯ § ∗ ³²´, ¯ ±...
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HW6 - MS&E 211 Linear& Nonlinear Optimization Fall...

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