28,832 research outputs found

    A Universal Catalyst for First-Order Optimization

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    main paper (9 pages) + appendix (21 pages)International audienceWe introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of theaccelerated proximal point algorithm. Our approach consists of minimizing a convex objective by approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. This strategy applies to a large class of algorithms, including gradient descent, block coordinate descent, SAG, SAGA, SDCA, SVRG, Finito/MISO, and their proximal variants. For all of these methods, we provide acceleration and explicit support for non-strongly convex objectives. In addition to theoretical speed-up, we also show that acceleration is useful in practice, especially for ill conditioned problems where we measure significant improvements

    A Universal Catalyst for First-Order Optimization

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    main paper (9 pages) + appendix (21 pages)International audienceWe introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of theaccelerated proximal point algorithm. Our approach consists of minimizing a convex objective by approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. This strategy applies to a large class of algorithms, including gradient descent, block coordinate descent, SAG, SAGA, SDCA, SVRG, Finito/MISO, and their proximal variants. For all of these methods, we provide acceleration and explicit support for non-strongly convex objectives. In addition to theoretical speed-up, we also show that acceleration is useful in practice, especially for ill conditioned problems where we measure significant improvements

    Catalyst Acceleration for Gradient-Based Non-Convex Optimization

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    We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed approach allows one to use them on weakly convex objectives, which covers a large class of non-convex functions typically appearing in machine learning and signal processing. In general, the scheme is guaranteed to produce a stationary point with a worst-case efficiency typical of first-order methods, and when the objective turns out to be convex, it automatically accelerates in the sense of Nesterov and achieves near-optimal convergence rate in function values. These properties are achieved without assuming any knowledge about the convexity of the objective, by automatically adapting to the unknown weak convexity constant. We conclude the paper by showing promising experimental results obtained by applying our approach to incremental algorithms such as SVRG and SAGA for sparse matrix factorization and for learning neural networks

    Inexact Model: A Framework for Optimization and Variational Inequalities

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    In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many known methods as a special case, the list including accelerated gradient method, composite optimization methods, level-set methods, proximal methods. The idea of the framework is based on constructing an inexact model of the main problem component, i.e. objective function in optimization or operator in variational inequalities. Besides reproducing known results, our framework allows to construct new methods, which we illustrate by constructing a universal method for variational inequalities with composite structure. This method works for smooth and non-smooth problems with optimal complexity without a priori knowledge of the problem smoothness. We also generalize our framework for strongly convex objectives and strongly monotone variational inequalities.Comment: 41 page

    CO-PrOx over nano-Au/TiO2: Monolithic catalyst performance and empirical kinetic model fitting

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    In this work, the performance of ceramic monoliths washcoated with Au/TiO2 is studied on CO preferential oxidation (CO-PrOx) reaction in H2-rich environments under a wide range of operating conditions of practical interest. The parameter estimation of a nonlinear kinetic empirical model representing this system is made via genetic algorithms by fitting the model predictions against our laboratory observations. Parameter uncertainty leading to inaccurate predictions is often present when kinetic models with nonlinear rate equations are considered. Here, after the fitting was concluded, a statistical study was conducted to determine the accuracy of the parameter estimation. Activation energies of ca. 30 kJ/mol and 55 kJ/mol were adjusted for CO and H2 oxidations, respectively. The catalyst showed appropriate activity and selectivity values on the CO oxidation on a H2-rich environment. After ca. 45 h on stream the catalyst showed no deactivation. Results show that the model is suitable for reproducing the behavior of the CO-PrOx reactions and it can be used in the design of reactors for hydrogen purification.Peer ReviewedPostprint (author's final draft

    Intensifying glycerol steam reforming on a monolith catalyst: a reaction kinetic model

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    In this work, a structured monolithic catalyst has been tested under a wide range of conditions (partial pressure, residence time, temperature and time-on-stream), with the aim of modeling its kinetic behavior and assessing its economic and upscaling potential. We have developed a sequential model to help us interpret both main trends and salient features. Unexpected behavior was found for certain parameter values, which led us to consider kinetic parasitic effects such as mass or heat transfer limitations. By independently invoking these effects, a conciliatory view of the results observed could not be reached. A combined explanation may prove successful, although overfitting could not be ruled out at this point. More importantly, however, the observed salient features of this stable and selective monolith catalyst may hold potential for process intensification of glycerol steam reforming, thus contributing to a more sustainable industry.Ministerio de Economía y Competitividad ENE2013-47880-C3-2-R, ENE2015-66975-C3-2-

    Design strategy and process optimization for reactors with continuous transport of an immobilized enzyme

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    In order to operate a process which uses immobilized enzymes at constant conversion and constant capacity, the refreshment of the enzyme must be continuous. In this paper, two reactor types with continuous refreshment of the biocatalyst are discussed: the stirred tank and the multistage fluidized bed. A method is presented for dimensioning a reactor in such a way that the costs for the conversion of substrate to product are minimized. These costs are calculated as the sum of the biocatalyst consumption and overall reactor costs.\ud \ud In contrast with the stirred-tank reactor, the multistage fluidized bed can be operated at a non-uniform temperature. For the glucose isomerase process, an optimal temperature gradient results in a small reduction in the biocatalyst consumption (±5%). It is concluded that, in general, a temperature gradient will only favour the economy of processes with relatively expensive biocatalysts.\ud \ud Compared with conventional reactor types, such as the continuous stirred-tank reactor and the fixed-bed reactor, the multistage fluidized-bed reactor can improve the economy of an enzyme-catalysed reaction significantly

    Catalytic Wet Air Oxidation of Aqueous Organic Mixtures

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    Catalytic Wet Air Oxidation (CWAO) has been investigated for the treatment of water contaminated by 4-hydroxybenzoic acid (4HBA) and equimolar mixture of phenol-4HBA. Both batch measurements for kinetics determination and continuous fixed bed operation have been performed on the same Activated Carbon (AC). After a fast initial deactivation AC was proved stable and efficient at moderate temperature and oxygen pressure, like for phenol degradation. The kinetic study in the case of highly adsorbing material as AC may require complex approach to account for the variation of adsorbed reactants during batch oxidation. Adsorption isotherms at reaction temperature and with aged AC have been obtained according to Langmuir equation and used in 4HBA mass balance to derive more significant kinetic parameters. At high catalyst loading and relatively low pollutant concentration, the variation of 4HBA during the batch may be even higher on the solid than in the aqueous phase
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