multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
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Figure 7.17 Close-up of Tubing Diameter Profile at Optimum. ..................................... 99<br />
Figure 7.18 Profile of Separator Pressure for Constant Tubing Diameter.......................... 100<br />
Figure 7.19 First Derivative of Separator Pressure. .................................................. 101<br />
Figure 7.20 Second Derivative of Separator Pressure. ............................................... 102<br />
Figure 7.21 First Derivative of Tubing Diameter...................................................... 103<br />
Figure 7.22 Second Derivative of Tubing Diameter................................................... 104<br />
Figure 7.23 Mixed-Partial Derivative of Tubing Diameter and Separator Pressure. .............. 105<br />
Figure 7.24 Minimum Eigenvalue of Hessian Matrix................................................. 107<br />
Figure 7.25 Maximum Eigenvalue of Hessian Matrix. ............................................... 108<br />
Figure 7.26 Curvature of Hessian Matrix. ............................................................. 109<br />
Figure 7.27 Convergence Path of Unmodified Newton’s Method.................................. 111<br />
Figure 7.28 Convergence Path of Modified Newton’s Method. .................................... 112<br />
Figure 7.29 Convergence Path of Polytope Heuristic, 2-D. ......................................... 113<br />
Figure 7.30 Convergence Path of Polytope Heuristic, 3-D. ......................................... 114<br />
Figure 7.31 Convergence Path of Triangular Polytopes.............................................. 115<br />
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