Abstract Motivated by localization problems such as cadastral maps refinements, we consider a generic Nonlinear Least Squares (NLS) problem of minimizing an aggregate squared fit across all nonlinear equations (measurements) with respect to the set of unknowns, e.g., coordinates of the unknown points’ locations. In a number of scenarios, NLS problems exhibit a nearly-separable structure: the set of measurements can be partitioned into disjoint groups (blocks), such that the unknowns that correspond to different blocks are only loosely coupled. We propose an efficient parallel method, termed Parallel Inexact Levenberg–Marquardt (PILM), to solve such generic large scale NLS problems. PILM builds upon the classical Levenberg–Marquard (LM) method, with a main novelty in that the nearly-block separable structure is leveraged in order to obtain a scalable parallel method. Therein, the problem-wide system of linear equations that needs to be solved at every LM iteration is tackled iteratively. At each (inner) iteration, the block-wise systems of linear equations are solved in parallel, while the problem-wide system is then handled via sparse, inexpensive inter-block communication. We establish strong convergence guarantees of PILM that are analogous to those of the classical LM; provide PILM implementation in a master-worker parallel computational environment; and demonstrate its efficiency on huge scale cadastral map refinement problems.

The proliferation of Big Data applications puts pressure on improving and optimizing the handling of diverse datasets across different domains. Among several challenges, major difficulties arise in data-sensitive domains like banking, telecommunications, etc., where strict regulations make very difficult to upload and experiment with real data on external cloud resources. In addition, most Big Data research and development efforts aim to address the needs of IT experts, while Big Data analytics tools remain unavailable to non-expert users to a large extent. In this paper, we report on the work-in-progress carried out in the context of the H2020 project I-BiDaaS (Industrial-Driven Big Data as a Self-service Solution) which aims to address the above challenges. The project will design and develop a novel architecture stack that can be easily configured and adjusted to address cross-sectoral needs, helping to resolve data privacy barriers in sensitive domains, and at the same time being usable by non-experts. This paper discusses and motivates the need for Big Data as a self-service, reviews the relevant literature, and identifies gaps with respect to the challenges described above. We then present the I-BiDaaS paradigm for Big Data as a self-service, position it in the context of existing references, and report on initial work towards the conceptual specification of the I-BiDaaS software architecture.