Saddle Point Conditions • Barrier Methods and Penalty/Augmented Lagrangian Methods

first-order, second-order necessary sufficiency under convexity Algorithms for Univariate Optimization bisection, Newton, safeguarded Newton, golden section search, Fibonacci rates of convergence Algorithms for Multivariate Optimization gradient methods: xk+1 = xk + αkdk important special case: xk+1 = xk − αkDk∇Tf(xk) choosing direction: steepest descent, Newton, quasi-Newton, conjugate gradient choosing the steplength: Armijo, linesearch the gradient-related condition and the general convergence theorem rates of convergenc