We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named SIFDecode and CUTEst, these updated versions feature ...dynamic memory allocation, a modern thread-safe Fortran modular design, a new Matlab interface and a revised installation procedure integrated with GALAHAD.
An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for unconstrained optimization, generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981, ...DAMTP, University of Cambridge), an algorithm by Nesterov and Polyak (Math Program 108(1):177–205, 2006) and a proposal by Weiser et al. (Optim Methods Softw 22(3):413–431, 2007). At each iteration of our approach, an approximate global minimizer of a local cubic regularisation of the objective function is determined, and this ensures a significant improvement in the objective so long as the Hessian of the objective is locally Lipschitz continuous. The new method uses an adaptive estimation of the local Lipschitz constant and approximations to the global model-minimizer which remain computationally-viable even for large-scale problems. We show that the excellent global and local convergence properties obtained by Nesterov and Polyak are retained, and sometimes extended to a wider class of problems, by our ARC approach. Preliminary numerical experiments with small-scale test problems from the CUTEr set show encouraging performance of the ARC algorithm when compared to a basic trust-region implementation.
An Adaptive Regularisation framework using Cubics (ARC) was proposed for unconstrained optimization and analysed in Cartis, Gould and Toint (Part I, Math Program, doi:
10.1007/s10107-009-0286-5
, ...2009), generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981, DAMTP, University of Cambridge), an algorithm by Nesterov and Polyak (Math Program 108(1):177–205, 2006) and a proposal by Weiser, Deuflhard and Erdmann (Optim Methods Softw 22(3):413–431, 2007). In this companion paper, we further the analysis by providing worst-case global iteration complexity bounds for ARC and a second-order variant to achieve approximate first-order, and for the latter second-order, criticality of the iterates. In particular, the second-order ARC algorithm requires at most
iterations, or equivalently, function- and gradient-evaluations, to drive the norm of the gradient of the objective below the desired accuracy
, and
iterations, to reach approximate nonnegative curvature in a subspace. The orders of these bounds match those proved for Algorithm 3.3 of Nesterov and Polyak which minimizes the cubic model globally on each iteration. Our approach is more general in that it allows the cubic model to be solved only approximately and may employ approximate Hessians.
In recent years, performance profiles have become a popular and widely used tool for benchmarking and evaluating the performance of several solvers when run on a large test set. Here we use data from ...a real application as well as a simple artificial example to illustrate that caution should be exercised when trying to interpret performance profiles to assess the relative performance of the solvers.
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•A method is developed to determine acid site densities on zeolites in solvents.•Extinction coefficients are zeolite-framework-independent and solvent-dependent.•Solvents have a major ...impact on measured acid site densities.
Fourier transform infrared (FTIR) spectroscopy is frequently used to characterize properties of catalytic sites, identify reaction intermediates, and probe interactions between adsorbates and surfaces, making it a versatile tool for elucidating reaction mechanisms in heterogeneous catalysis. While this technique is typically regarded as qualitative or semiquantitative in nature, quantitative results can be obtained by determining integrated molar extinction coefficients (IMECs), or the amount of signal per mole of adsorbed or bulk species. IMECs for vibrational modes corresponding to pyridine adsorbed onto Brønsted and Lewis acid sites have been determined in the vapor phase; however, the effect of solvents on catalytic sites cannot be captured. Liquid-phase IMECs enable quantification of adsorbates in the presence of solvents, allowing quantitative evaluations of the effect of solvents on catalysts. A method is outlined for determining IMECs of pyridine adsorbed on zeolites in the liquid phase in an attenuated total reflection (ATR) configuration. The method can also be applied to substrates other than pyridine. The IMECs for pyridine adsorbed onto Brønsted and Lewis acid sites in water, acetonitrile, and ethanol are determined. The IMEC values are shown to be dependent on solvent choice, but independent of zeolite framework.
Solvent selection is a pressing challenge in developing efficient and selective liquid phase catalytic processes, as predictive understanding of the solvent effect remains lacking. In this work, an ...attenuated total reflection infrared spectroscopy technique is developed to quantitatively measure adsorption isotherms on porous materials in solvent and decouple the thermodynamic contributions of van der Waals interactions within zeolite pore walls from those of pore-phase proton transfer. While both the pore diameter and the solvent identity dramatically impact the confinement (adsorption) step, the solvent identity plays a dominant role in proton-transfer. Combined computational and experimental investigations show increasingly favorable pore-phase proton transfer to pyridine in the order: water < acetonitrile < 1,4 - dioxane. Equilibrium methods unaffected by mass transfer limitations are outlined for quantitatively estimating fundamental thermodynamic values using statistical thermodynamics.
Due to the low volatility and highly oxygenated nature of biomass derived feedstocks, biomass upgrade reactions are frequently conducted in the presence of solvent to improve substrate mass transfer ...to the catalyst surface. However, relevant catalyst characterization techniques are most often performed in vacuum or inert gas environments, where the effect of solvent on the catalytic sites is ignored. Comparatively, characterization techniques in the presence of solvent are relatively rare, which poses challenges in developing structure-activity relationships for liquid phase reactions. In this perspective, commonly utilized techniques for probing the solid-liquid interface are briefly covered, with a focus on the role of solvent on zeolite and solid acid catalysis. New applications of techniques are proposed, most notably with ATR-FTIR, in the context of extracting thermodynamic information for the further understanding of the role of solvent on broadly applicable catalyst properties, such as acidity, and to develop structure-activity relationships for solid catalysts in solvent.
Due to the low volatility and highly oxygenated nature of biomass derived feedstocks, biomass upgrade reactions are frequently conducted in the presence of solvent to improve substrate mass transfer to the catalyst surface.
We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it is ...unaffected by the nonsmoothness of the objective in that a first-order trust-region or quadratic regularization method applied to it takes at most $\mathcal{O}(\epsilon^{-2})$ function evaluations to reduce the size of a first-order criticality measure below $\epsilon$. Specializing this result to the case when the composite objective is an exact penalty function allows us to consider the objective- and constraint-evaluation worst-case complexity of nonconvex equality-constrained optimization when the solution is computed using a first-order exact penalty method. We obtain that in the reasonable case when the penalty parameters are bounded, the complexity of reaching within $\epsilon$ of a KKT point is at most $\mathcal{O}(\epsilon^{-2})$ problem evaluations, which is the same in order as the function-evaluation complexity of steepest-descent methods applied to unconstrained, nonconvex smooth optimization. PUBLICATION ABSTRACT
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•Characterization of NaY in liquid water with a novel FTIR spectroscopic method.•Lewis acidic zeolite NaY protonates pyridine in liquid water at room temperature.•The NaY Brønsted ...site only protonates substrates with sufficient basicity.•Motivates catalyst characterization under liquid phase reaction conditions.
Liquid phase catalyst characterization is experimentally challenging, but it deserves consideration because solvent choice can affect catalyst structure and acidity. Thus, in vacuo spectroscopy of adsorbed probe molecules such as pyridine, while valuable, may provide incomplete information on available catalytic sites in liquid phase reactions. To this end, an Attenuated Total Reflection Fourier Transform Infrared spectroscopy (ATR-FTIR) cell was used to detect pyridine adsorbed on sodium exchanged faujasite (NaY) in liquid water. The slow accumulation of pyridinium on NaY in the presence of liquid water was observed, suggesting water promotes the protonation of pyridine on NaY, a Lewis acidic material. Transmission FTIR and ATR-FTIR experiments revealed that pyridinium concentration increased with increasing amount of water in NaY, making the liquid phase technique more apt than the established vacuum technique for observing the effect of water on the acid sites of NaY. However, the Brønsted catalyzed ring opening of 2,5-dimethylfuran (DMF) to 2,5-hexanedione is not active on NaY in water. The lack of activity is attributed to the low basicity of DMF. This is consistent with the observation that acetonitrile, a weaker base than pyridine, was not protonated on NaY in water, while 2,6-dimethylpyridine, a stronger base than pyridine, was readily protonated. Thus, although NaY is capable of forming pyridinium in water, NaY may not be active with respect to Brønsted catalyzed pathways unless a reactant is sufficiently basic. Results presented in this work suggest that probe molecule choice can lead to different interpretations of the nature of acid sites in the presence of adsorbed, and especially liquid, water.
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