Complexity of trust-region methods with unbounded Hessian approximations for smooth and nonsmooth optimization

We develop a worst-case evaluation complexity bound for trust-region methodsin the presence of unbounded Hessian approximations. We use the algorithm ofarXiv:2103.15993v3 as a model, which is designed for nonsmooth regularizedproblems, but applies to unconstrained smooth problems as a special case. Ouranalysis assumes that the growth of the Hessian approximation is controlled bythe number of successful iterations. We show that the best known complexitybound of $\epsilon^{-2}$ deteriorates to $\epsilon^{-2/(1-p)}$, where $0 \le p< 1$ is a parameter that controls the growth of the Hessian approximation. Thefaster the Hessian approximation grows, the more the bound deteriorates. Weconstruct an objective that satisfies all of our assumptions and for which ourcomplexity bound is attained, which establishes that our bound is sharp. To thebest of our knowledge, our complexity result is the first to considerpotentially unbounded Hessians and is a first step towards addressing aconjecture of Powell [38] that trust-region methods may require an exponentialnumber of iterations in such a case. Numerical experiments conducted in doubleprecision arithmetic are consistent with the analysis.

Dynamic-threshold-based pre-relaying for enhanced key allocation in quantum-secured networks

Quantum key distribution (QKD) is experiencing a rapid increase of interest due to its security advantages in the face of quantum computers. However, typical QKD deployments are point-to-point and limited in terms of distance, which significantly restricts their utilization for end-user applications. To overcome these restrictions, trusted relays are adopted as intermediate nodes to allow the transition to QKD networks (QKDNs), where one of the hallmarks is the key management system. In this work, we investigate different key allocation strategies as a method to enhance the performance of key management systems in QKDN from the perspective of key allocation success rate and key delivery delay. We first describe an upgrade model from classical to QKDN at three distinct network layers—quantum, key management, and service. Then, we propose a novel, to our knowledge, key allocation strategy leveraging the benefits of key storage and relaying as a solution to improve the QKDN performance. To achieve this, our method makes use of end-to-end virtual quantum key pools (VQKPs) implemented between non-adjacent nodes requesting key material. We introduce static and dynamic upper and lower threshold limits at the VQKP level, with the dynamic thresholds adapted according to application demand, to control the key distribution in the network and fill the pools ahead of end-user requests. We demonstrate through simulations that the introduction of thresholds achieves performance enhancement and explain the trade-off between the key allocation success rate and key delivery delay evaluation metrics in comparison with different on-demand key allocation strategies.

Design and Performance of the ALPS II Regeneration Cavity

Impact of Financial Incentives and Department Size on Scholarly Activity Output

Use of assistive technology to assess distal motor function in subjects with neuromuscular disease

The effect of prenatal balanced energy and protein supplementation on gestational weight gain: An individual participant data meta-analysis in low- and middle-income countries

Beyond pleasurable and meaningful: Psychologically rich entertainment experiences

Net buffer load during regional citrate anticoagulated continuous renal replacement therapy

Low agreement and frequent invalid controls in two SARS-CoV-2 T-cell assays in people with compromised immune function

Correction: Neural recordings can differentiate between spontaneously metastasizing melanomas and melanomas with low metastatic potential