We give a derivation of the result for the rate of linear convergence in p. 4 of the paper. Consider an objective function f to be minimized using a search direction obtained from Bkpk = −∇f(xk) where Bk = B(xk) is a positive definite partial Hessian for k = 0, 1, 2,... Under the assumptions of theorem 3.1 in the paper, xk converges to a stationary point x∗. Assume that B(x) is Lipschitz continuous in the region of interest (that is, ∃L> 0: ‖B(x)−B(y) ‖ ≤ L ‖x − y ‖ for any two points x, y in the region) with bounded condition number, and that we take unit steps in the line search. Then: xk + pk − x ∗ = xk − x ∗ −B−1
The problem under consideration is the nonlinear optimization problem min f(x) text{ subject to } x ...
An example of slow convergence for Newton’s method on a function with globally Lipschitz continuous ...
The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a com...
Cover title.Includes bibliographical references (leaves 20-21).Research supported by the U.S. Army R...
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence r...
All norms in this section are defined elementwise. To recap, we solve the following problem: min ‖X‖...
6 pagesWe give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of...
We extend the previous analysis of Schmidt et al. [2011] to derive the linear convergence rate obtai...
Suppose that E is a real normed linear space, C is a nonempty convex subset of E, T:C→C is a Lipschi...
Many problems in data science (e.g. machine learning, optimization and statistics) can be cast as lo...
Let [a,b] ⊂ Rand let {Lj}j ε{lunate} N be a sequence of positive linear operators from Cn + 1([a, b]...
© 2017 Springer Science+Business Media, LLC The proximal point algorithm (PPA) has been well studie...
AbstractThis note investigates the convergence of a linear stationary iterative process of the form ...
The global optimization problem min f(x), x in S with S=[a,b], a, b in Rn and f(x) satisfying the L...
The nonlinear minimization problem is to find a (local) minimizer for an objective function f(·), wh...
The problem under consideration is the nonlinear optimization problem min f(x) text{ subject to } x ...
An example of slow convergence for Newton’s method on a function with globally Lipschitz continuous ...
The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a com...
Cover title.Includes bibliographical references (leaves 20-21).Research supported by the U.S. Army R...
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence r...
All norms in this section are defined elementwise. To recap, we solve the following problem: min ‖X‖...
6 pagesWe give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of...
We extend the previous analysis of Schmidt et al. [2011] to derive the linear convergence rate obtai...
Suppose that E is a real normed linear space, C is a nonempty convex subset of E, T:C→C is a Lipschi...
Many problems in data science (e.g. machine learning, optimization and statistics) can be cast as lo...
Let [a,b] ⊂ Rand let {Lj}j ε{lunate} N be a sequence of positive linear operators from Cn + 1([a, b]...
© 2017 Springer Science+Business Media, LLC The proximal point algorithm (PPA) has been well studie...
AbstractThis note investigates the convergence of a linear stationary iterative process of the form ...
The global optimization problem min f(x), x in S with S=[a,b], a, b in Rn and f(x) satisfying the L...
The nonlinear minimization problem is to find a (local) minimizer for an objective function f(·), wh...
The problem under consideration is the nonlinear optimization problem min f(x) text{ subject to } x ...
An example of slow convergence for Newton’s method on a function with globally Lipschitz continuous ...
The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a com...