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

On the Complexity of Scheduling

A note on event-based MILP models for resource-constrained project scheduling problems

For the nonpreemptive two machine job-shop scheduling problem with a fixed number of jobs and objective functions Σfi and maxfi, wherefi are nondecreasing functions of the finish times of jobsi, polynomial algorithms are presented. This answers previous open questions about the complexity status of the corresponding problems with objective functionsLmax, ΣwiUi, and ΣwiU. We generalize these results by showing that the problem with any regular criterion can be solved in polynomial time.

Fur das Zweimaschinen-Job-Shop-Problem ohne Arbeitsunterbrechnungen und den Zielfunktionen Σfi bzw. maxfi, wobei diefi monotone Funktionen der Fertigstellungszeiten der Jobsi sind, werden fur den Fall fester Jobanzahlen polynomiale Algorithmen angegeben. Dies beantwortet insbesondere die bislang offene Frage nach dem Komplexitatsstatus des obigen Problems fur die ZielfunktionenLmax, ΣwiUi, und ΣwiU. Schlieβlich zeigen wir, daβ das Problem mit beliebiger regularer Zielfunktion ebenfalls polynomial losbar ist.

On the complexity of two machine job-shop scheduling with regular objective functions

AnO (nlogn)-algorithm is given for the two-machine, job-shop scheduling problem withn unit-time tasks in which maximum lateness is to be minimized. This algorithm generalizes recent results by Hefetz and Adiri for the corresponding makespan problem.

Minimizing maximum lateness in a two-machine unit-time job shop

This paper has two parts. In the first part (Section 2 to 5), we discuss complexity issues for deterministic scheduling problems and their implications. These issues reflect the current trend in the scheduling literature. The second part (Section 6), is devoted to a practical case study.

Peter Brucker

Papers

On the Complexity of Scheduling

A note on event-based MILP models for resource-constrained project scheduling problems

On the complexity of two machine job-shop scheduling with regular objective functions

Minimizing maximum lateness in a two-machine unit-time job shop

Scheduling: Theory and Applications