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Unconstrained Optimization p
Optimization Over a Convex Set p
Lagrange Multiplier Theory p
7 other sections not shown
active constraints affine scaling akdk algorithm analysis Appendix approximation Armijo rule assume assumption augmented Lagrangian bounded computation conjugate gradient method constant stepsize constrained problem constraint set continuously differentiable convergence rate convex function convex set coordinate corresponding cost function defined denote descent direction diagonal direction dk dual function dual problem eigenvalues equality constraints equation example Exercise exists f(xk feasible direction finite given global minimum gradient projection method Hessian Hessian matrix inequality constraints interior point interior point methods iteration Lagrange multiplier Lagrangian limit point linear programming manifold matrix minimization rule Newton's method nonlinear obtain optimal solution optimality conditions penalty function positive definite problem minimize f(x proof quadratic program rate of convergence satisfies scalar second order Section sequence xk Show solving stationary point steepest descent stepsize rule subgradient subset subspace superlinear unconstrained variables vector x'Qx xfc+i xk+i zero