Chemical Engineering Hand Written_Notes_Part_118

Chemical Engineering Hand Written_Notes_Part_118 - 238 5....

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238 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES 11. Summary In these lecture notes, we have presented various numerical schemes based on multivariate unconstrained optimization formulation. One of the major appli- cation of unconstrained optimization is function approximation or multivariate regression. Thus, we begin by providing a detailed description of the model pa- rameter estimation problem. We then derive necessary and su cient conditions for optimality for a general multivariable unconstrained optimization problem. If the model has some nice structure, such as it is linear in parameters, then the parameter estimation problem can be solved analytically. Thus, the linear model parameter estimation (linear regression) problem is treated elaborately. Geometric and statistical properties of the linear least square problem are dis- cussed in detail to provide further insights into this formulation. Numerical methods for estimating parameters of the nonlinear-in-parameter models are
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Chemical Engineering Hand Written_Notes_Part_118 - 238 5....

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