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

Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems

A branch and bound algorithm for a single-machine scheduling problem with positive and negative time-lags

In a job-shop scheduling problem we have n jobs J 1,...,J n to be processed on m different machines M l,...,M m . Each job J; consists of a number n i of operations \( \left( {i = 1,...,n;j,...,{n_i}} \right).\) which have to be processed in this order. Operations O ij can be processed only by one machine μ ij (i = 1,..., n; j i = 1,..., n i ). Denote by pi, the corresponding processing time. We assume that all processing times are integer numbers.

The job-shop problem and immediate selection

Equal-processing-time scheduling problems whose complexity status has been unknown are shown to be solved in polynomial time by well-known and relatively new techniques. Single-machine, parallel-machine, parallel-batch, open-shop, flow-shop and job-shop environments are touched upon.

Ten notes on equal-processing-time scheduling

In a multi-processor-tasks job-shop problem (MPTJSP) there is a machine set associated with each operation. All machines are needed for the whole processing period to process the operation. The objective is to find a schedule which minimizes the makespan. In a multi-mode job-shop problem (MMJSP) there is a set of machine sets associated with each operation. One has to assign a machine set to each operation and to solve the resulting MPTJSP such that the resulting makespan is minimized. For the MMJSP a tabu-search algorithm is presented. Computational results are reported.

Peter Brucker

Papers

Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems

A branch and bound algorithm for a single-machine scheduling problem with positive and negative time-lags

The job-shop problem and immediate selection

Ten notes on equal-processing-time scheduling

Tabu-search for the multi-mode job-shop problem