- On Nesterov's Smooth Chebyshev-Rosenbrock Function Florian Jarre (jarreopt.uni-duesseldorf.de) Abstract: We discuss a modification of the chained Rosenbrock function introduced by Nesterov, a polynomial of degree four of $n$ variables. Its only stationary point is the global minimizer with optimal value zero. An initial point is given such that any continuous piecewise linear descent path consists of at least an exponential number of $0.72 \cdot 1.618^{n}$ linear segments before reducing the function value by 75\%. Moreover, there exists a uniform bound, independent of $n$, on the Lipschitz constant of the first and second derivatives of this modified Rosenbrock function along a descent path. Keywords: Rosenbrock function, descent path. Category 1: Nonlinear Optimization (Unconstrained Optimization ) Citation: Technical Report, Dept. of Mathematics, University of Duesseldorf, May 2011 Download: [PDF]Entry Submitted: 05/31/2011Entry Accepted: 05/31/2011Entry Last Modified: 07/15/2011Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.