We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning. Metaphorically, the adaptation allows us to find needles in haystacks in the form of very predictive but rarely seen features. Our paradigm stems from recent advances in stochastic optimization and online learning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. We give several efficient algorithms for empirical risk minimization problems with common and important regularization functions and domain constraints. We experimentally study our theoretical analysis and show that adaptive subgradient methods outperform state-of-the-art, yet non-adaptive, subgradient algorithms.

Adaptive Subgradient Methods for Online Learning and Stochastic Optimization.

/pdf/adaptive-subgradient-methods-for-online-learning-and-1nnwnbmnxy.pdf

Adaptive Subgradient Methods for Online Learning and Stochastic Optimization

https://sci2s.ugr.es/sites/default/files/files/Teaching/GraduatesCourses/Metaheuristicas/Bibliography/VNS.pdf

Variable neighborhood search

Variable Neighborhood Search.

Network function virtualization (NFV) has drawn significant attention from both industry and academia as an important shift in telecommunication service provisioning. By decoupling network functions (NFs) from the physical devices on which they run, NFV has the potential to lead to significant reductions in operating expenses (OPEX) and capital expenses (CAPEX) and facilitate the deployment of new services with increased agility and faster time-to-value. The NFV paradigm is still in its infancy and there is a large spectrum of opportunities for the research community to develop new architectures, systems and applications, and to evaluate alternatives and trade-offs in developing technologies for its successful deployment. In this paper, after discussing NFV and its relationship with complementary fields of software defined networking (SDN) and cloud computing, we survey the state-of-the-art in NFV, and identify promising research directions in this area. We also overview key NFV projects, standardization efforts, early implementations, use cases, and commercial products.

/pdf/network-function-virtualization-state-of-the-art-and-29gg3feprt.pdf

Network Function Virtualization: State-of-the-Art and Research Challenges

A Decomposition, Construction and Post-processing Approach for a Specific Nurse Rostering Problem

The problem of scheduling identical jobs with chain precedence constraints on two uniform machines is considered. It is shown that the corresponding makespan problem can be solved in linear time.

Scheduling identical jobs with chain precedence constraints on two uniform machines

We prove that the problem P ∣ pi = p, pmtn ∣ ∑wiUi is unary NP-hard although the corresponding nonpreemptive problem can be solved in O(n log n) time, where n is the number of jobs. This contrasts the fact that usually preemptive problems are not harder than their nonpreemptive counterparts.

Scheduling Equal Processing Time Jobs to Minimize the Weighted Number of Late Jobs

We consider the following version of the auditing problem. A set of jobs must be processed by auditors A1,...,Am. Each job consists of several tasks and there may be precedence constraints between these tasks. There is a due date associated with each job. Each auditor is available during disjoint time periods. Furthermore, s/he has a minimal and maximal working time. If task i is assigned to an auditor Aj, the processing time is pij and the processing costs are cij. A task assigned to auditor Aj can be preempted only at the end of one of the working periods of Aj. In this case it must be continued at the beginning of the next period.



One has to assign the tasks to the auditors and find a feasible schedule for the assigned tasks for each auditor such that the sum of the assignment costs and a weighted sum of tardiness values is minimized.



A tabu search procedure for this problem is described and computational results are presented. Copyright © 1999 John Wiley & Sons, Ltd.

Peter Brucker

Papers

A Decomposition, Construction and Post-processing Approach for a Specific Nurse Rostering Problem

Scheduling identical jobs with chain precedence constraints on two uniform machines

Scheduling Equal Processing Time Jobs to Minimize the Weighted Number of Late Jobs

A new tabu search procedure for an audit-scheduling problem

k-optimal solution sets for some polynomially solvable scheduling problems