Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping

We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas laid out in [H. Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order $O(t^{-2})$ for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.Comment: 25 pages, 3 Figure

Ideas and perspectives: climate-relevant marine biologically driven mechanisms in Earth system models

The current generation of marine biogeochemical modules in Earth system models (ESMs) considers mainly the effect of marine biota on the carbon cycle. We propose to also implement other biologically driven mechanisms in ESMs so that more climate-relevant feedbacks are captured. We classify these mechanisms in three categories according to their functional role in the Earth system: (1) "biogeochemical pumps", which affect the carbon cycling; (2) "biological gas and particle shuttles", which affect the atmospheric composition; and (3) "biogeophysical mechanisms", which affect the thermal, optical, and mechanical properties of the ocean. To resolve mechanisms from all three classes, we find it sufficient to include five functional groups: bulk phyto- and zooplankton, calcifiers, and coastal gas and surface mat producers. We strongly suggest to account for a larger mechanism diversity in ESMs in the future to improve the quality of climate projections

A multiobjective continuation method to compute the regularization path of deep neural networks

Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of relevant features), and robustness. In machine learning approaches based on linear models, it is well known that there exists a connecting path between the sparsest solution in terms of the $\ell^1$ norm (i.e., zero weights) and the non-regularized solution, which is called the regularization path. Very recently, there was a first attempt to extend the concept of regularization paths to DNNs by means of treating the empirical loss and sparsity ($\ell^1$ norm) as two conflicting criteria and solving the resulting multiobjective optimization problem. However, due to the non-smoothness of the $\ell^1$ norm and the high number of parameters, this approach is not very efficient from a computational perspective. To overcome this limitation, we present an algorithm that allows for the approximation of the entire Pareto front for the above-mentioned objectives in a very efficient manner. We present numerical examples using both deterministic and stochastic gradients. We furthermore demonstrate that knowledge of the regularization path allows for a well-generalizing network parametrization.Comment: 7 pages, 6 figure

Detectability of Artificial Ocean Alkalinization and Stratospheric Aerosol Injection in MPI‐ESM

To monitor the success of carbon dioxide removal (CDR) or solar radiation management (SRM) that offset anthropogenic climate change, the forced response to any external forcing is required to be detectable against internal variability. Thus far, only the detectability of SRM has been examined using both a stationary and nonstationary detection and attribution method. Here, the spatiotemporal detectability of the forced response to artificial ocean alkalinization (AOA) and stratospheric aerosol injection (SAI) as exemplary methods for CDR and SRM, respectively, is compared in Max Planck Institute Earth System Model (MPI-ESM) experiments using regularized optimal fingerprinting and single-model estimates of internal variability, while working under a stationary or nonstationary null hypothesis. Although both experiments are forced by emissions according to the Representative Concentration Pathway 8.5 (RCP8.5) and target the climate of the RCP4.5 scenario using AOA or SAI, detection timescales reflect the fundamentally different forcing agents. Moreover, detectability timescales are sensitive to the choice of null hypothesis. Globally, changes in the CO2 system in seawater are detected earlier than the response in temperature to AOA but later in the case of SAI. Locally, the detection time scales depend on the physical, chemical, and radiative impacts of CDR and SRM forcing on the climate system, as well as patterns of internal variability, which is highlighted for oceanic heat and carbon storage

Multiobjective Optimization of Non-Smooth PDE-Constrained Problems

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization"

Conciencia tributaria y su incidencia en la evasión de tributos del sector hospedajes Carhuaz, 2016

La investigación titulada "Conciencia tributaria y su incidencia en la evasión de tributos del sector hospedajes Carhuaz, 2016". Fue elaborado con el propósito de describir si la conciencia tributaria incide en la evasión tributaria del sector hospedajes de la ciudad de Carhuaz. El tipo de estudio es de acuerdo a la técnica de contrastación, fue una investigación descriptiva y correlacional, El diseño de la investigación fue no experimental, por el periodo de estudio es transaccional o transversal ya que se analizaron las variables solamente en el año 2016. Se aplicó una encuesta a una población de 17 hospedajes tantos hoteles, hostales y alojamientos, los resultados fueron procesados con el programa Excel, y en relación al resultado se realizó su respectivo análisis e interpretación. Los resultados de la presente investigación contribuirán a un mejor control de parte de la Administración Tributaria a fin de tener fundamentos para reorientar a las empresas de servicio como lo son los hospedajes, así mismo servirá a los profesionales para una futura investigaciónTesi

An event model for WS-BPEL 2.0

This report presents an engine-independent WS-BPEL 2.0 event model. It supports both passive monitoring and active control of process execution by external applications. Some of the assumptions in the presented event model are inspired by a particular implementation, e.g. fault handling and compensation; however they are kept as general as possible, so that they can be mapped on other engine-specific approaches to tackle faults and support compensation. In addition, the report draws on the experience of some of the authors in business process management and software development. The overall BPEL event model consists of a set of event models for the different types of BPEL entities that change their states: processes, process instances, general activities, scope activities, invoke activities, loops, links, variables, partner links, and correlation sets. The event model is used by the authors of the report in several projects, all utilizing process life cycle events in different scenarios