The Geometry of Monotone Operator Splitting Methods

We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through monotonicity-preserving operations, is seldom solvable in its original form. We embed it in an auxiliary space, where it is associated with a surrogate monotone inclusion problem with a more tractable structure and which allows for easy recovery of solutions to the initial problem. The surrogate problem is solved by successive projections onto half-spaces containing its solution set. The outer approximation half-spaces are constructed by using the individual operators present in the model separately. This geometric framework is shown to encompass traditional methods as well as state-of-the-art asynchronous block-iterative algorithms, and its flexible structure provides a pattern to design new ones

Tools and Algorithms for the Construction and Analysis of Systems

This book is Open Access under a CC BY licence. The LNCS 11427 and 11428 proceedings set constitutes the proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019. The total of 42 full and 8 short tool demo papers presented in these volumes was carefully reviewed and selected from 164 submissions. The papers are organized in topical sections as follows: Part I: SAT and SMT, SAT solving and theorem proving; verification and analysis; model checking; tool demo; and machine learning. Part II: concurrent and distributed systems; monitoring and runtime verification; hybrid and stochastic systems; synthesis; symbolic verification; and safety and fault-tolerant systems

DIVE on the internet

This dissertation reports research and development of a platform for Collaborative Virtual Environments (CVEs). It has particularly focused on two major challenges: supporting the rapid development of scalable applications and easing their deployment on the Internet. This work employs a research method based on prototyping and refinement and promotes the use of this method for application development. A number of the solutions herein are in line with other CVE systems. One of the strengths of this work consists in a global approach to the issues raised by CVEs and the recognition that such complex problems are best tackled using a multi-disciplinary approach that understands both user and system requirements. CVE application deployment is aided by an overlay network that is able to complement any IP multicast infrastructure in place. Apart from complementing a weakly deployed worldwide multicast, this infrastructure provides for a certain degree of introspection, remote controlling and visualisation. As such, it forms an important aid in assessing the scalability of running applications. This scalability is further facilitated by specialised object distribution algorithms and an open framework for the implementation of novel partitioning techniques. CVE application development is eased by a scripting language, which enables rapid development and favours experimentation. This scripting language interfaces many aspects of the system and enables the prototyping of distribution-related components as well as user interfaces. It is the key construct of a distributed environment to which components, written in different languages, connect and onto which they operate in a network abstracted manner. The solutions proposed are exemplified and strengthened by three collaborative applications. The Dive room system is a virtual environment modelled after the room metaphor and supporting asynchronous and synchronous cooperative work. WebPath is a companion application to a Web browser that seeks to make the current history of page visits more visible and usable. Finally, the London travel demonstrator supports travellers by providing an environment where they can explore the city, utilise group collaboration facilities, rehearse particular journeys and access tourist information data

DISTRIBUTED DETERMINISTIC ASYNCHRONOUS ALGORITHMS IN TIME-VARYING GRAPHS THROUGH DYKSTRA SPLITTING

10.1137/18M1168297SIAM JOURNAL ON OPTIMIZATION291484-51