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Basic Concepts l
Functions of One Variable
Unconstrained Functions of N Variables
5 other sections not shown
active constraints aerodynamic aircraft airfoil analysis approach approximation techniques calculate Chap coefficient concepts consider constraint boundary constraint functions convergence convex defined dependent variables design problem design space design variables dual methods efficiency equality constraints Equation estimate example exterior penalty function feasible directions Figure find the minimum function evaluations geometry given by Eq golden section method Hessian matrix hypersphere improve inequality constraints iteration Kuhn-Tucker conditions Lagrange multipliers Lagrangian linear programming load method of feasible minimization problem Newton's method nonlinear Nonlinear Programming number of design numerical optimization objective function one-dimensional search optimization process optimization techniques optimum design penalty function polynomial interpolation primal quadratic quadratic approximation reduced gradient method search direction shown in Fig side constraints simplex algorithm slack variables solution solve specified stress structural optimization subproblem Taylor series tion truss two-variable function space unconstrained minimization update upper bound vector VF(X zero