NLP Models 2 - 1.1 N. L. P. Formulation examples...

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Unformatted text preview: 1.1 N. L. P. Formulation examples & techniques Katta G. Murty, IOE 611 Lecture slides Rectangular Rail Car Design: Top & bottom sheet $325/m 2 . Siding sheet $175/m 2 . Volume should ≥ 1000 m 3 . Height should ≤ 3 m. Total area of sides should ≤ 75 m 2 . Find min cost design. Simple Portfolio Model: Data b = budget ($ available to invest) n = number investment opportu. available μ j = expected fraction return in j th op- portu., j = 1 to n D = n × n variance-covariance matrix of fraction returns. ( μ j ) , D usually estimated from past data. Actual returns random variables. Two important objective functions. One to max expected return. 2nd to min risk, mea- sured by variance of total fraction return. 18 Banks, mutual fund operators use models like this (mostly based on QP models) to plan investments. 19 Curve Fitting, Parameter estimation in non- linear modeling In above, objective and constraint functions came with prob- lem. Not common in NLP modeling. In most, functional forms of objective and constraint functions to be determined empirically. This work called Curve Fitting . Two phases in it. Phase I: Select Model Function: Either based on theo- retical considerations, or by guessing suitable one looking at plots of data....
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NLP Models 2 - 1.1 N. L. P. Formulation examples...

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