Error bound and exact penalty method for optimization problems with nonnegative orthogonal constraint

This paper is concerned with a class of optimization problems with the nonnegative orthogonal constraint, in which the objective function is $L$-smooth on an open set containing the Stiefel manifold ${\rm St}(n,r)$. We derive a locally Lipschitzian error bound for the feasible points without zero rows when $n>r>1$, and when $n>r=1$ or $n=r$ achieve a global Lipschitzian error bound. Then, we show that the penalty problem induced by the elementwise $\ell_1$-norm distance to the nonnegative cone is a global exact penalty, and so is the one induced by its Moreau envelope under a lower second-order calmness of the objective function. A practical penalty algorithm is developed by solving approximately a series of smooth penalty problems with a retraction-based nonmonotone line-search proximal gradient method, and any cluster point of the generated sequence is shown to be a stationary point of the original problem. Numerical comparisons with the ALM \citep{Wen13} and the exact penalty method \citep{JiangM22} indicate that our penalty method has an advantage in terms of the quality of solutions despite taking a little more time.Comment: 34 pages, and 6 figure

A relaxation method for binary orthogonal optimization problems with its applications

This paper focuses on a class of binary orthogonal optimization problems frequently arising in semantic hashing. Consider that this class of problems may have an empty feasible set, rendering them not well-defined. We introduce an equivalent model involving a restricted Stiefel manifold and a matrix box set, and then investigate its penalty problems induced by the $\ell_1$-distance from the box set and its Moreau envelope. The two penalty problems are always well-defined, and moreover, they serve as the global exact penalties provided that the original model is well-defined. Notably, the penalty problem induced by the Moreau envelope is a smooth optimization over an embedded submanifold with a favorable structure. We develop a retraction-based nonmonotone line-search Riemannian gradient method to address this penalty problem to achieve a desirable solution for the original binary orthogonal problems. Finally, the proposed method is applied to supervised and unsupervised hashing tasks and is compared with several popular methods on the MNIST and CIFAR-10 datasets. The numerical comparisons reveal that our algorithm is significantly superior to other solvers in terms of feasibility violation, and it is comparable even superior to others in terms of evaluation metrics related to the Hamming distance.Comment: Binary orthogonal optimization problems, global exact penalty, relaxation methods, semantic hashin

Hybrid Data-driven Framework for Shale Gas Production Performance Analysis via Game Theory, Machine Learning and Optimization Approaches

A comprehensive and precise analysis of shale gas production performance is crucial for evaluating resource potential, designing field development plan, and making investment decisions. However, quantitative analysis can be challenging because production performance is dominated by a complex interaction among a series of geological and engineering factors. In this study, we propose a hybrid data-driven procedure for analyzing shale gas production performance, which consists of a complete workflow for dominant factor analysis, production forecast, and development optimization. More specifically, game theory and machine learning models are coupled to determine the dominating geological and engineering factors. The Shapley value with definite physical meanings is employed to quantitatively measure the effects of individual factors. A multi-model-fused stacked model is trained for production forecast, on the basis of which derivative-free optimization algorithms are introduced to optimize the development plan. The complete workflow is validated with actual production data collected from the Fuling shale gas field, Sichuan Basin, China. The validation results show that the proposed procedure can draw rigorous conclusions with quantified evidence and thereby provide specific and reliable suggestions for development plan optimization. Comparing with traditional and experience-based approaches, the hybrid data-driven procedure is advanced in terms of both efficiency and accuracy.Comment: 37 pages, 15 figures, 6 table

Isotopic evidence for quasi-equilibrium chemistry in thermally mature natural gases

Natural gas is a key energy resource, and understanding how it forms is important for predicting where it forms in economically important volumes. However, the origin of dry thermogenic natural gas is one of the most controversial topics in petroleum geochemistry, with several differing hypotheses proposed, including kinetic processes (such as thermal cleavage, phase partitioning during migration, and demethylation of aromatic rings) and equilibrium processes (such as transition metal catalysis). The dominant paradigm is that it is a product of kinetically controlled cracking of long-chain hydrocarbons. Here we show that C₂₊ n-alkane gases (ethane, propane, butane, and pentane) are initially produced by irreversible cracking chemistry, but, as thermal maturity increases, the isotopic distribution of these species approaches thermodynamic equilibrium, either at the conditions of gas formation or during reservoir storage, becoming indistinguishable from equilibrium in the most thermally mature gases. We also find that the pair of CO₂ and C₁ (methane) exhibit a separate pattern of mutual isotopic equilibrium (generally at reservoir conditions), suggesting that they form a second, quasi-equilibrated population, separate from the C₂ to C₅ compounds. This conclusion implies that new approaches should be taken to predicting the compositions of natural gases as functions of time, temperature, and source substrate. Additionally, an isotopically equilibrated state can serve as a reference frame for recognizing many secondary processes that may modify natural gases after their formation, such as biodegradation

Elucidating the hydrotropism behaviour of aqueous caffeine and sodium benzoate solution through NMR and neutron total scattering analysis

Hydrotropism is a convenient way to increase the solubility of drugs by up to several orders of magnitude, and even though it has been researched for decades with both experimental and simulation methods, its mechanism is still unknown. Here, we use caffeine/sodium benzoate (CAF-SB) as model system to explore the behaviour of caffeine solubility enhancement in water through NMR spectroscopy and neutron total scattering. 1H NMR shows strong interaction between caffeine and sodium benzoate in water. Neutron total scattering combined with empirical potential structure refinement, a systematic method to study the solution structure, reveals π-stacking between caffeine and the benzoate anion as well as Coulombic interactions with the sodium cation. The strongest hydrogen bond interaction in the system is between benzoate and water, which help dissolve CAF-SB complex and increase the solubility of CAF in water. Besides, the stronger interaction between CAF and water and the distortion of water structure are further mechanisms of the CAF solubility enhancement. It is likely that the variety of mechanisms for hydrotropism shown in this system can be found for other hydrotropes, and NMR spectroscopy and neutron total scattering can be used as complementary techniques to generate a holistic picture of hydrotropic solutions

Isotopic evidence for quasi-equilibrium chemistry in thermally mature natural gases

Natural gas is a key energy resource, and understanding how it forms is important for predicting where it forms in economically important volumes. However, the origin of dry thermogenic natural gas is one of the most controversial topics in petroleum geochemistry, with several differing hypotheses proposed, including kinetic processes (such as thermal cleavage, phase partitioning during migration, and demethylation of aromatic rings) and equilibrium processes (such as transition metal catalysis). The dominant paradigm is that it is a product of kinetically controlled cracking of long-chain hydrocarbons. Here we show that C₂₊ n-alkane gases (ethane, propane, butane, and pentane) are initially produced by irreversible cracking chemistry, but, as thermal maturity increases, the isotopic distribution of these species approaches thermodynamic equilibrium, either at the conditions of gas formation or during reservoir storage, becoming indistinguishable from equilibrium in the most thermally mature gases. We also find that the pair of CO₂ and C₁ (methane) exhibit a separate pattern of mutual isotopic equilibrium (generally at reservoir conditions), suggesting that they form a second, quasi-equilibrated population, separate from the C₂ to C₅ compounds. This conclusion implies that new approaches should be taken to predicting the compositions of natural gases as functions of time, temperature, and source substrate. Additionally, an isotopically equilibrated state can serve as a reference frame for recognizing many secondary processes that may modify natural gases after their formation, such as biodegradation

Rapid Evaporation of Water on Graphene/Graphene-Oxide: A Molecular Dynamics Study

To reveal the mechanism of energy storage in the water/graphene system and water/grapheme-oxide system, the processes of rapid evaporation of water molecules on the sheets of graphene and graphene-oxide are investigated by molecular dynamics simulations. The results show that both the water/graphene and water/grapheme-oxide systems can store more energy than the pure water system during evaporation. The hydroxyl groups on the surface of graphene-oxide are able to reduce the attractive interactions between water molecules and the sheet of graphene-oxide. Also, the radial distribution function of the oxygen atom indicates that the hydroxyl groups affect the arrangement of water molecules at the water/graphene-oxide interface. Therefore, the capacity of thermal energy storage of the water/graphene-oxide system is lower than that of the water/graphene system, because of less desorption energy at the water/graphene-oxide interface. Also, the evaporation rate of water molecules on the graphene-oxide sheet is slower than that on the graphene sheet. The Leidenfrost phenomenon can be observed during the evaporation process in the water/grapheme-oxide system