Nonlinear programming: analysis and methods
Classical optimization - unconstrained and equality constrained problems; Optimality conditions for constrained extrema; Convex sets and functions; Duality in nonlinear convex programming; Generalized convexity; Analysis of selected nonlinear programming problems; One-dimensional optimization; Multidimensional unconstrained optimization without derivative: empirical and conjugate direction methods; Second derivative, steepest descent and conjugate gradient methods; Variable metric algorithms; Penalty function methods; Solution of constrained problems by extensions of unconstrained optimization techniques; Approximation-type algorithms.
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OPTIMALITY CONDITIONS FOR CONSTRAINED
CONVEX SETS AND FUNCTIONS
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approximation assume Avriel chapter compute concave functions conjugate directions conjugate functions constrained problems constraint qualification continuously differentiable convergence convex programs convex set D+f(x defined derivatives descent method dual program duality equations Example exists feasible set finite follows func function evaluations given global minimum Hence Hessian matrix Huang's family hyperplane inequality iteration Kuhn-Tucker Lagrange multipliers Lagrangian Lemma Let f line searches linear program linearly independent Math necessary conditions Newton's method nonempty Nonlinear Programming nonnegative objective function obtain optimal solution penalty function penalty function methods points xl positive definite positive number primal programming problem Proof proper convex function pseudoconvex quadratic function quadratic program quadratic termination quasiconvex function reader real-valued function satisfying search directions solving steepest descent step length sufficient conditions Suppose symmetric Theorem tion unconstrained minimization unconstrained optimization updating formula variable metric algorithms variable metric methods vector xTQx