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General Schemes for Investigating
Influence of Noise
11 other sections not shown
algorithm arbitrary argmin augmented Lagrangian auxiliary problem bounded computation condition number conditions of Theorem conjugate gradient method constraints construct convergence rate convex function convex set derivatives df(x dual problem equations estimate example Exercise exists extremum conditions fk(x formula function f(x geometric progression Hence inequality initial approximation Lagrange multipliers Lemma Let f(x linear programming linear programming problem Lipschitz condition mathematical matrix method 13 method converges methods for solving neighborhood Newton's method nonempty nonsingular minimum point number of steps objective function obtain optimization problems parameters point of f(x primal problem of minimizing proof Prove quadratic function quasi-Newton methods random noise rate of convergence rate of geometric satisfies a Lipschitz Section 1.4 sequence set Q sharp minimum simplex method smooth solution strictly convex subgradient method sufficiently small tion unique values variables variant vector x e Q