Optimization Methods for Engineering Design |
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16 pages matching Kuhn-Tucker conditions in this book
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Contents
Introduction to the Formulation of Optimization Problems | 1 |
Unconstrained Minimization | 38 |
conjugate gradients | 87 |
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2-bar truss A₁ active constraints algorithm analysis apply approach approximation assume basic feasible solution block Chapter components conjugate gradient method consider constraint functions constraint surfaces contours convergence convex criterion defined derivatives design problem design variables discussed eigenvalue equations example F₁ feasible region Figure finite difference formula function evaluations given idea inequality interior penalty function interpolation iteration Kuhn-Tucker conditions Lagrange multiplier linear programming matrix method of feasible mini minimization methods minimizing step negative nonlinear Nonlinear Programming Note objective function obtain optimization problem optimum design penalty function method pivot positive definite possible post office parcel produce programming problem quadratic relative minima requires S₁ satisfied scalar shown in Fig situation slack variables solve starting point steepest descent straints stress structure Taylor series technique tion unconstrained minimization variable metric vector x₁ Xq+1 y₁ zero