Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions

Optimization ◽  
2010 ◽  
Vol 59 (5) ◽  
pp. 661-676 ◽  
Author(s):  
Jein-Shan Chen ◽  
Shaohua Pan
Keyword(s):  
Lipschitz Continuity ◽  
Merit Functions ◽  
Parametric Class

scholarly journals Convergence Rates for Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions

2019 ◽  
Vol 374 (2) ◽  
pp. 823-871 ◽  
Author(s):  
Simon Becker ◽  
Nilanjana Datta
Keyword(s):  
Convergence Rates ◽  
Lipschitz Continuity ◽  
Open Quantum Systems ◽  
High Energy ◽  
Quantum Systems ◽  
Quantum Evolution ◽  
Infinite Dimensions ◽  
Quantum Brownian Motion ◽  
Infinite Dimensional ◽  
Energy Constrained

Abstract By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite dimensions, which are stronger than previously known bounds. We extensively discuss applications of our theory to quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. Next, we obtain explicit log-Lipschitz continuity bounds for entropies of infinite-dimensional quantum systems, and classical capacities of infinite-dimensional quantum channels under energy-constraints. These bounds are determined by the high energy spectrum of the underlying Hamiltonian and can be evaluated using Weyl’s law.

The Preservation of Continuity and Lipschitz Continuity by Optimal Reward Operators

2004 ◽  
Vol 29 (3) ◽  
pp. 672-685 ◽  
Author(s):  
Rida Laraki ◽  
William D. Sudderth
Keyword(s):  
Lipschitz Continuity ◽  
Optimal Reward

scholarly journals Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry

2012 ◽  
Vol 18 (4) ◽  
pp. 825-837 ◽  
Author(s):  
Raf Cluckers ◽  
Immanuel Halupczok
Keyword(s):  
Lipschitz Continuity
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