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Due to their unique physiochemical properties that may be tailored for specific purposes, ionic liquids (ILs) have been investigated for various applications, including chemical separations, catalysis, energy storage, and space propulsion. The different cations and anions comprising ILs may be selected to optimize a range of desired properties, such as thermal stability, ionic conductivity, and volatility, leading to the designation of certain ILs as designer "green" solvents. The effect of counterions on the properties of ILs is of both fundamental scientific interest and technological importance. Herein, we report a systematic experimental and theoretical investigation of the size, charge, stability toward dissociation, and geometric/electronic structure of 1-ethyl-3-methyl imidazolium (EMIM)-based IL clusters containing two different atomic counterions (i.e., bromide [Br−] and iodide [I−]). This work extends our studies of EMIM+ cations with atomic chloride (Cl−) and molecular tetrafluoroborate (BF4−) anions reported previously by Baxter et al. [Chem. Mater. 34, 2612 (2022)] and Zhang et al. [J. Phys. Chem. Lett. 11, 6844 (2020)], respectively. Distributions of anionic IL clusters were generated in the gas phase using electrospray ionization and characterized by high mass resolution mass spectrometry, energy-resolved collision-induced dissociation, and negative ion photoelectron spectroscopy experiments. The experimental results reveal anion-dependent trends in the size distribution, relative abundance, ionic charge state, stability toward dissociation, and electron binding energies of the IL clusters. Complementary global optimization theory provides molecular-level insights into the bonding and electronic structure of a selected subset of clusters, including their low energy structures and electrostatic potential maps, and how these fundamental characteristics are influenced by anion substitution. Collectively, our findings demonstrate how the fundamental properties of ILs, which determine their suitability for many applications, may be tuned by substituting counterions. These observations are critical in the sub-nanometer cluster size regime where phenomena do not scale predictably to the bulk phase, and each atom counts toward determining behavior. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) is a widely used statistical technique for dimensionality reduction, extracting a low-dimensional subspace in which the variance is maximised (or the reconstruction error is minimised). To improve the interpretability of learned representations, several variants of PCA have recently been developed to estimate the principal components with a small number of input features (variable), such as sparse PCA and group sparse PCA. However, most existing methods suffer from either the requirement of measuring all the input variables or redundancy in the set of selected features. Another challenge for these methods is that they need to specify the sparsity level of the coefficient matrix in advance. To address the above issues, in this paper, we propose an elastic-net regularisation for sparse group PCA (ESGPCA), which incorporates sparsity constraints into the objective function to consider both within-group and between-group sparsities. Such a sparse learning approach allows us to automatically discover the sparse principal loading vectors without any prior assumption of the input features. We solve the non-smooth regularised problem using the alternating direction method of multipliers (ADMM), an efficient distributed optimisation technique. Empirical evaluations on both synthetic and real datasets demonstrate the effectiveness and promising performance of our sparse group PCA than other compared methods. [ABSTRACT FROM AUTHOR]

Today, supply chains (SCs) have been struggling with a new type of disruption known as outbreaks such as epidemics or pandemics. This type of disruption has features such as long-term and uncertain lifespan and leads to severe fluctuations in product demand. This paper elaborates on a hybrid approach based on artificial neural networks (ANN) and mathematical programming techniques to efficiently deal with this type of disruption in the production planning of SCs. In the first phase of the hybrid approach, a multi-layer perceptron ANN model with an optimised structure is developed to efficiently predict the demand and its peak points. In the second phase, the predicted demands are considered as input in a new multiobjective agile recovery production planning model. The proposed model minimises total costs and delivery times and maximises responsiveness. A real case study in Iran is conducted to verify and validate the proposed hybrid approach. The prediction error of the ANN method is about 1 percent. According to the predicted demand, optimal decisions are determined by the proposed model. The impact of under-estimation and over-estimation of demand is evaluated in terms of total costs, delivery time, responsiveness and shortage costs in the SCs. [ABSTRACT FROM AUTHOR]

The trend of reverse globalisation prompts manufacturing enterprises to adopt distributed structures with multiple factories for improving production efficiency, meeting customer requirements, and responding disturbance events. This study focuses on scheduling a distributed flexible job shop with random job processing time to achieve minimal makespan and minimal total tardiness. First, a stochastic programming model is established to formulate the concerned problems. Second, in accordance with the natures of two objectives and randomness, an evolutionary algorithm incorporating an evaluation method is designed. In it, population-based and external archive-based search processes are developed for searching candidate solutions, and the evaluation method integrates stochastic simulation and discrete event simulation to calculate objective values of acquired solutions. Finally, a mathematical optimisation solver, CPLEX, is employed to validate the developed model and optimisation approach. A set of cases is solved to verify the performance of the proposed method. The comparisons and discussions show the superiority of the proposed method for handling the problems under study. [ABSTRACT FROM AUTHOR]

In many settings, fleets of assets must perform series of missions with in-between finite breaks. For such fleets, a widely used maintenance strategy is the fleet selective maintenance (FSM). Under resource constraints, the FSM problem selects an optimal subset of feasible maintenance actions to be performed on a subset of components to minimise the maintenance cost while ensuring high system reliability during the upcoming mission. The majority of extant FSMP models are focussed on traditional physics-based reliability models. With recent advances in Machine Learning (ML) and Deep Learning (DL) algorithms, data-driven methods have shown accuracy in predicting remaining useful life (RUL). This paper proposes a predictive FSM strategy for fleets of complex and large multicomponent systems. It relies on a concurrent ML/DL and optimisation approach where a clustering algorithm is used to determine the health states of components and a probabilistic RUL prognostics model is used for component reliability assessment. An optimisation model is developed to solve the predictive FSM problem to ensure high reliability of all systems within the fleet. An efficient two-phase solution approach is developed to solve this complex optimisation problem. Numerical experiments show the validity of the approach and highlight the improved maintenance plans achieved. [ABSTRACT FROM AUTHOR]

In the manufacturing industry, timely order fulfilment from diverse customers is important for operational profitability, given the constraints of limited production capacity. This paper proposes a novel queueing system for a production system, in which order processing times are categorised as regular or rush based on customer preference. The proposed queueing system employs variable service rates and service strategies in conjunction with staggered production to deal with heterogeneous arrivals. We compute the steady-state probability distribution and develop system performance indicators. The lower and upper bounds of the expected sojourn time for rush and regular orders are derived. Numerical results show that an appropriate switching policy can reduce rush orders by approximately 35% while regular orders increase by less than 10%, demonstrating significant improvement in order fulfilment management. We formulate a multi-objective optimisation problem and implement the NSGA-II algorithm to obtain Pareto optimal solutions. Finally, three regression models are proposed to determine the minimum cost and the associated optimal service rates, given the maximum acceptable value of the expected number of rush orders. The established models can explain at least 80% of the dataset of the optimal solutions and thus our numerical findings provide useful guidance for decision-makers and production managers. [ABSTRACT FROM AUTHOR]

As the EU and the US successively proposed the carbon border adjustment mechanism (CBAM) and the Clean Competition Act (CCA), importers are now required to declare the carbon emissions of their products. Particularly, wheel companies face increasing time pressure with the gradual development of implementation paths for net-zero emissions and implementing carbon pricing policies in various countries. This research uses the production data of Taiwan wheel companies to establish a mathematical model for the activity-based cost optimisation decision-making process. It explores the impact of different carbon emission costs on a company's product mix with pricing decisions. Further, the research proposes five mathematical programmes for single-period cost optimisation decision-making under carbon pricing. These models provide some detailed view, such as changes in profits and product mix caused by high carbon taxes or other changes for each resource. Furthermore, the production cost optimal model proposed in this research can be used by enterprises to fulfill their social responsibilities while ensuring profitability and serve as a reference for making net-zero transformation decisions. [ABSTRACT FROM AUTHOR]

This paper offers an in-depth examination of the ergonomics of human-centred assembly systems in Industry 4.0, where manual tasks remain essential. The use of advanced technologies such as motion capture (MOCAP) and virtual reality (VR) is analysed as ways to enhance system efficiency and improve worker well-being. The paper highlights the importance of optimising assembly system performance while considering both economic and human factors. Metrics to assess ergonomic risk and productivity are discussed based on human-centred technologies, and existing operational research models are explored to analyse how human factors could be considered in optimising system performance. Additionally, the paper explores potential future directions and how they could play a role in Industry 4.0. [ABSTRACT FROM AUTHOR]

This paper aims to propose a Novel Condition-based maintenance (CBM) decision aid model for optimising the maintenance of complex multi-component systems. As the degradation level of each component is assumed to be independent and stochastic, it follows a specific probability distribution determined from historical data of experimental observations and inspection. The main objective is to optimise the total cost for providing maintenance actions and reducing the excess of spare parts usage. The decision support model consists of determining measurements on components with the aim of estimating the instant of time of removing predictively one or a group of components before they fail. The measurement model includes the mean residual lifetime (MRL) and some extensions developed for this purpose. For demonstrating the pertinency of the proposed model, we use a preventive maintenance strategy for one-component systems and a grouping/opportunistic maintenance for multi-component systems. Besides, a numerical comparative study performing these measurements is carried out using several examples and a case study from Electric energy distribution systems. The solution is illustrated as a decision-making optimal model for optimising the maintenance operations' costs and the total number of spare parts. The numerical results and the comparison show the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Raman spectroscopy has been more widely used recently in the quality detection of dairy products. Because Raman spectroscopy can conduct rapid analyses of small sample sizes at high dimensions, its use in the dairy industry is becoming a hot topic for researchers. To improve the robustness and accuracy of logistic regression identification method, a new Raman spectroscopy identification method was proposed that combines a distributionally robust optimization technique and fused lasso technique with logistic regression. Then, Raman spectroscopy was used to analyze two types of dairy products that were collected for antijamming identification testing to verify the effectiveness of the new method. The experimental results show that the proposed method is more robust and has a higher recognition accuracy than the traditional logistic regression., As one of the important food sources for humans, dairy products are regularly consumed globally. Recently, the dairy industry has seen an increase in the sale of wantonly counterfeit dairy [...]

Libcint is a library designed for the evaluation of analytical integrals for Gaussian type orbitals. It prioritizes simplicity, ease of use, and efficiency for the development of quantum chemistry programs. In the release of version 6.0, Libcint supports the computation of integrals for various operators, such as overlap, Coulomb, Gaunt, Breit, attenuated Coulomb, Slater-type geminals, and Yukawa potential, as well as arbitrary orders of derivatives for these operators. To enhance the usability of the library, Libcint provides a uniform function signature for all integral functions. A code generator is included to automate the implementation of new integrals. To achieve better performance on modern central processing unit architectures, the library employs explicit single instruction multiple data parallelization in the code implementation. [ABSTRACT FROM AUTHOR]

This work describes optimizations of N-electron system wave functions by means of the simulated annealing technique within the doubly occupied configuration interaction framework. Using that technique, we minimize the energy variance of a Hamiltonian, providing determinations of wave functions corresponding to ground or excited states in an identical manner. The procedure that allows us to determine electronic spectra can be performed using treatments of restricted or unrestricted types. The results found in selected systems, described in terms of energy, spin, and wave function, are analyzed, showing the performance of each method. We also compare these results with those arising from more traditional approaches that minimize the energy, in both restricted and unrestricted versions, and with those obtained from the full configuration interaction treatment. [ABSTRACT FROM AUTHOR]

This work presents four mixed integer linear programming (MILP) models for the assembly flow shop problem in order to minimize the makespan. This production environment has two stages: production and assembly. The first stage consists of different machines designed to manufacture parts of a product. The second stage is intended for a final assembly. The performance measure considered is highly essential for industries from different segments, as it focuses on the best use of the time available for production. Statistical analysis with different tools was used to assess the performance and efficiency of mathematical models, emphasizing the analysis of performance profiles. Results showed that mathematical models are efficient, and the position-based model presented the best results for small and large instances during computational experimentation. All mathematical models can be used as direct tools in decision-making for the production sequencing problem in the approached environment. [ABSTRACT FROM AUTHOR]

This paper introduces novel mathematical optimisation models for the 2-Dimensional guillotine Cutting Stock Problem with Variable-Sized Stock that appears in a Spanish company in the honeycomb cardboard industry. This problem mainly differs from the classical cutting stock problems in the stock, which is considered variable-sized, i.e. we have to decide the panel dimensions, width, and length. This approach is helpful in industries where the stock is produced simultaneously with the cutting process. The stock is then cut into smaller rectangular pieces that must meet the customers' requirements, such as the type of item, dimensions, demands, and technical specifications. Furthermore, in the problem tackled in this paper, the cuts are guillotine, performed side to side. The proposed mathematical models are validated using real data from the company, obtaining results that drastically reduce the produced material and leftovers, reducing operation times and economic costs. [ABSTRACT FROM AUTHOR]

This paper presents a new scheme for energy-efficient clustering in Internet of Things (IoT) networks by employing an optimized evolutionary rate water cycle algorithm (OERWCA), aiming to address crucial issues, such as energy conservation measured through average energy consumption per node, network longevity quantified by total operational rounds until node depletion, and throughput as an indicator of data transmission efficiency. In OERWCA, a local escaping operator (LEO) is introduced to avoid algorithm trapping in local optima by enhancing its exploration capability. Besides, advanced control-randomization operators balance exploration and exploitation dynamically for efficient search behavior in the solution space. The algorithm optimizes cluster head selection by minimizing energy consumption and redundant transmission. Simulations comparing OERWCA with previous optimization methods, including NCCLA, FHHO, and EACH-COA, demonstrate the superior performance of the proposed algorithm. Key metrics evaluated include network lifetime, throughput, average transmission delay, packet delivery ratio (PDR), and energy efficiency. OERWCA achieves significant improvements, including up to a 26% increase in network lifetime, a 32% boost in throughput, a 20% reduction in transmission delay, and a 27% enhancement in PDR compared to the best-performing benchmarks. These results highlight OERWCA's effectiveness in optimizing critical performance parameters for IoT networks. The enhanced convergence properties of the proposed algorithm also address some common limitations found in existing methods. This work, therefore, provides a robust solution toward extending the operational lifetime of IoT networks, which is one of the fundamental steps forward in large-scale efficient resource management. [ABSTRACT FROM AUTHOR]

The turbocharged dual-fuel engine is modeled and connected online to optimiser platform for transient input variation of input parameters decided by designed algorithms. This task is undertaken to enable intelligent control of the propulsion system including the Hydrogen injection instantly to reduce the thermal irreversibility. Therefore, two methods of optimisation are applied to data collected from a turbocharged dual fuel operated propulsion system with direct diesel fuel injection and hydrogen port injection. This study investigates the application of multi-objective game theory (MOGT) and non-dominated sorting genetic algorithm II (NSGA-II) for optimising the performance of a diesel-hydrogen dual-fuel engine. The system is designed in 1D framework with input variability of the turbocharger efficiency, hydrogen mass injection, air compression ratio (Rp), and start of combustion (SoC). The objective is to set maximized the volume work while minimising the entropy generation and NO emission. The first populations in the optimisation procedures are initialised with uniform Latin hypercube and random space filler design of experiment (DoE) for both optimisers. The MOGT can find the best solution faster than NSGA-II with slightly better result. The statistics showed that MOGT generates 12 more unfeasible designs that do not meet the constraint limit on NO emission. The findings indicate that for different optimisation algorithms there are some factors with different effect direction and size on the objectives. Additionally, it is discovered that although MOGT solution makes higher objective function value, the NSGA-II optimal solution leads to better engine efficiency and lower fuel consumption. [Display omitted] • Turbocharged dual-fuel diesel-H2 engine 1D simulation and data processing. • MOGT and NSGA-II competition for optimal engine operation redesign. • MOGT funds optimal case in early design compared to genetic algorithm optimiser. • The optimisation is set to maximise work output, while minimise NO and entropy. • H2 injection is the most influential parameter on entropy based on MOGT. [ABSTRACT FROM AUTHOR]

Injection molding (IM) is a rapid process that injects molten plastic into a mold cavity for cooling and solidification. It is widely used in daily necessities, auto parts, medical equipment, electronic products, and infant toys. However, the process parameters of IM are complex and interact with each other. IM simulation software can not only provide optimized solutions to process problems, but also improve the quality of manufactured parts. This study report combines Taguchi design and computational software (Moldflow, MINITAB, and MATLAB) to analyze and simulate the process parameters of the back cover of the LCD monitor to obtain its minimum warpage (W) in z-direction. The results of Taguchi design (traditional optimization technique) show that the optimal processing parameter combination to obtain W is 40°C of mold temperature (A1), 220°C of plastic temperature (B1), 70 MPa of packing pressure (C1), 5 s of holding time (D3), 20 s of cooling time (E1), 60 cm3/s of injection speed (F1), 40% of switch position (G1), and 90 MPa of the injection pressure (H3), named as A1B1C1D3E1F1G1H3. Four important parameters (B, C, D, and G) were obtained by Taguchi design in IM process. The computed warpage errors, obtained by Moldflow software and regression analysis, are less than 2.5%. However, Taguchi design can only result in an optimal set of combinations of specified processing parameters. The particle swarm optimization (PSO) algorithm, which is a non-traditional optimization technique, often overcomes obstacles faced by Taguchi design. The examined warpage errors through Moldflow software and PSO are less than 3.5%. It is shown that the combination of Taguchi design and PSO algorithm is very suitable for processing optimization of IM production. Its smart manufacturing method can not only reduce production costs and time, but also increase the flexibility of processing parameter selection to a greater extent. [ABSTRACT FROM AUTHOR]

Stochastic Block Models (SBMs) have emerged as a powerful framework for modelling community structures in networks. However, accurately determining the number of communities in SBMs remains challenging. In this paper, we propose a novel approach for community detection in stochastic block models through penalized variational estimation. Our method introduces two penalties on the variational objective function to ensure elimination of redundant blocks. We present the variational computing procedure, and demonstrate through simulation and empirical analysis that our approach can effectively identifies community structures and achieves accurate parameter estimation simultaneously. [ABSTRACT FROM AUTHOR]

This work presents a knowledge-based decision-making robust antenna design (KDRAD) method that employs a heuristic-optimisation technique for antenna design. The method is used to create and scale a single-element antenna to operate at multiple frequencies within the 5 G range. In this study, a low-profile planar four-element microstrip antenna of 14.8 mm × 14.8 mm × 0.508 mm gives simulated and measured impedance bandwidths of about 1.18 GHz (26.43–27.61 GHz) and 1.08 GHz (26.42–27.50 GHz), respectively, with a centre frequency of 27 GHz. The mm-wave planar four-port antenna has a maximum gain of 7.2 dBi; isolation of 33.2 dB; and multiple antenna matrices with minimal ECC (0.000000109), high diversity gain (10 dB) and channel capacity loss of 0.00110 bits/s/Hz. [ABSTRACT FROM AUTHOR]

Once the efficiency of solar energy-converting devices depends on the population of the electron–hole pairs (excitons), one way of increasing the conversion efficiency of photoactive materials is using electron-accepting materials, which acts on the separation efficiency of these pairs by collecting the electrons. In such a way, carbon nitride (C3N4) has been studied as an electron acceptor. With simple synthesis and easy tailoring properties, this material becomes a promising candidate in organic photovoltaic cells. Thus, the objective was to evaluate the photocurrent as a function of exciton properties. Then, P3HT was obtained by redox polymerization and C3N4 by urea pyrolysis. Photoelectrochemical and spectroscopic measurements were performed to characterize the electrodes. In addition, theoretical calculations were carried out using TD-DFT. It was observed that a photocurrent 3-fold increased in relation to the pure P3HT film (from 12.1 up to 33.2 µA cm-2), attributed to the increase in the hole-electron separation efficiency, with an increase in their lifetime (from 0.18 to 0.42 ms). The electron transport was also boosted (an increase of 2.1 × 10-3 cm2 V-1 s-1). The theoretical calculations suggest that the structural modification of C3N4 affects the photocurrent due to the charge delocalization induced by the torsion of the triazine units. Besides, the photocurrent values achieved in this work were not expressive; the results pointed out that the association P3HT+C3N4 is promissory. The further optimization of these systems by heat treatment, type of solvent, and deposition method could lead to better results. Additionally, the theoretical results demonstrated that minor system modifications could improve the photocurrent values. The synergetic effect of the composite obtained between poly(3-hexylthiophene) and carbon nitride in the appropriate proportion leads to a 3-fold increase in photocurrent due to the improvement in the properties of the photogenerated excintons. [ABSTRACT FROM AUTHOR]

In this article, we study an inventory model for a single perishable item which can contribute to economic growth, organizational benefit as well as individual life. Both supplier and retailer consider price discount for defective items up to a specified percentage, in a situation where the parameters involved are vague and imprecise. Such consideration has not been reported in the literature. By recognizing the power of neutrosophic environment to handle uncertainty and impreciseness inherited or existing in the problem, we use single-valued triangular neutrosophic numbers (SVNs) for representing stock-based demand, retail price, ordering cost, holding cost, wastage cost, imperfect item price, and preservation cost with de-neutrosophication. The Taylor series approximation is used to transform the time variables in the profit function into the order quantity and maximum stock variables. We determine the theoretical optimality condition and verify the concavity and uniqueness of the global optimal solution using Hessian matrix. Our aim is to determine the maximum value of the retailer's profit by making decisions on the order quantity and maximum stock level, as well as to estimate shortages, stock-out time, cycle length, and identify the model's inherent impreciseness. We develop neutrosophic fuzzy optimization technique (NeFOT), an extension of the intuitionistic fuzzy optimization technique (IFOT) to evaluate the compromise acceptance, indeterminacy, and rejection levels inherited in the model and optimal solution. We support the study by illustrating a numerical example and graph with Mathematica 11.3 and LINGO 18.0. [ABSTRACT FROM AUTHOR]

Low efficiency affects energy-demanding systems such as water distribution networks (WDNs). In these systems, the pressure typically is maintained below the switch using regulators to minimize water loss from leaks. Utilizing energy production equipment may be an effective way to reduce water waste, while also producing energy, although its viability depends on how much energy can be recovered. A water distribution system's design is a combinatorial issue, which typically has a larger number of local optima. Consequently, hybrid metaheuristic and heuristic processes can explore the solution with less computational time requirements to gain deep understanding of the problem structure and specific characteristics of the problem. However, these outcomes have an enormous computational burden because of the relatively large number of hydraulic simulations. This investigated where pressure-reducing valves (PRVs) and pumps as turbines (PATs) should be placed in a network that distributes water. The study suggests a deterministic mathematical optimization technique for minimizing the price of WDNs utilizing recognized recognized pipe distances and a defined range of commercially obtainable sizes. A novel heuristic mixed-integer nonlinear programming technique (H-MINLP) with a beleaguered path search process is used to perform optimization. Based on the evaluation of the ideal trajectories in which water flows in a WDN. Two distinct subroutines work together to decrease the sizes of network pipes methodically and sequentially, and effectively exploit the search space. There are no parameters to adjust in the new method, and therefore it does not require a consequential purpose. In addition, a graph clustering technique is utilized to increase the heuristic approach's performance by simplifying its convergence. Compared with other methods in the literature, this hybrid optimization ensures good solutions in terms of energy and water savings. According to the findings, compared with other research on the same network, the proposed optimization decreased leakage by 21%. [ABSTRACT FROM AUTHOR]

In this paper, we study the distributed optimisation problem in an iterative environment, where the global objective function consists of agents' local objective functions, and each agent with the local objective function performs repeated tasks in finite time. The objective is to minimise the global objective function by the local communication of agents in the repeated running system. To solve this problem, we propose a distributed optimisation algorithm based on iterative learning methods that combines the terminal iterative learning strategy with the subgradient strategy. When the initial states of all agents are the same in each iteration, by the proposed algorithm, it is proved that all agents' states asymptotically converge to the optimal solution. Moreover, considering that the initial states of agents in each iteration may not be accurately measured, we further study the distributed optimisation problem under different initial states. We find that all agents' states asymptotically converge to the neighbourhood of the optimal solution. Finally, the effectiveness of the algorithm is verified by the numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, we deal with nonconvex fractional programming problems involving E-differentiable functions (F P E) . The so-called E-Karush-Kuhn-Tucker sufficient E-optimality conditions are established for nonsmooth optimization problems under E-univexity hypothesis. The established optimality conditions are explained with a numerical example. The so-called vector dual problem in the sense of Schaible (S D E) involves E-differentiable functions for (F P E) is defined under E-univexity hypothesis. [ABSTRACT FROM AUTHOR]

We study second-order differential sensitivity in parametrized vector optimization problems with inclusion constraints. First, we consider a set-valued unconstrained problem and establish a sufficient condition for the second-order directional Dini derivative of the marginal map to be equal to the minimum of that of the objective map. We then extend our research to vector optimization problems with general inclusion constraints and demonstrate that the first- and second-order directional Dini derivatives of the objective image map are equal to the union of those of the objective map. Using advanced proof techniques, we derive a formula for the second-order directional Dini derivative of the marginal map and prove the second-order semi-derivability of the feasible objective and marginal/efficient-value maps. Examples are provided to illustrate the novelty and depth of our results. [ABSTRACT FROM AUTHOR]

Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation, namely, the linear optimization relaxation given by the reformulation–linearization technique, the Shor relaxation, and the relaxation resulting from their combination. We establish several structural properties of these relaxations in relation to the corresponding relaxations of StQPs without any sparsity constraints, and pay particular attention to the rank-one feasible solutions retained by these relaxations. We then utilize these relations to establish several results about the quality of the lower bounds arising from different relaxations. We also present several conditions that ensure the exactness of each relaxation. [ABSTRACT FROM AUTHOR]

Commonly, decomposition and splitting techniques for optimization problems strongly depend on convexity. Implementable splitting methods for nonconvex and nonsmooth optimization problems are scarce and often lack convergence guarantees. Among the few exceptions is the Progressive Decoupling Algorithm (PDA), which has local convergence should convexity be elicitable. In this work, we furnish PDA with a descent test and extend the method to accommodate a broad class of nonsmooth optimization problems with non-elicitable convexity. More precisely, we focus on the problem of minimizing the difference of convex and weakly convex functions over a linear subspace. This framework covers, in particular, a family of stochastic programs with nonconvex recourse and statistical estimation problems for supervised learning. [ABSTRACT FROM AUTHOR]

Computing the approximation quality is a crucial step in every iteration of sandwiching algorithms (also called Benson-type algorithms) used for the approximation of convex Pareto fronts, sets or functions. Two quality indicators often used in these algorithms are polyhedral gauge and epsilon indicator. In this article, we develop an algorithm to compute the polyhedral gauge and epsilon indicator approximation quality more efficiently. We derive criteria that assess whether the distance between a vertex of the outer approximation and the inner approximation needs to be recalculated. We interpret these criteria geometrically and compare them to a criterion developed by Dörfler et al. for a different quality indicator using convex optimization theory. For the bi-criteria case, we show that only two linear programs need to be solved in each iteration. We show that for more than two objectives, no constant bound on the number of linear programs to be checked can be derived. Numerical examples illustrate that incorporating the developed criteria into the sandwiching algorithm leads to a reduction in the approximation time of up to 94 % and that the approximation time increases more slowly with the number of iterations and the number of objective space dimensions. [ABSTRACT FROM AUTHOR]

The derivative-free projection method (DFPM) is an effective and classic approach for solving the system of nonlinear monotone equations with convex constraints, but the global convergence or convergence rate of the DFPM is typically analyzed under the Lipschitz continuity. This observation motivates us to propose an inertial hybrid DFPM-based algorithm, which incorporates a modified conjugate parameter utilizing a hybridized technique, to weaken the convergence assumption. By integrating an improved inertial extrapolation step and the restart procedure into the search direction, the resulting direction satisfies the sufficient descent and trust region properties, which independent of line search choices. Under weaker conditions, we establish the global convergence and Q-linear convergence rate of the proposed algorithm. To the best of our knowledge, this is the first analysis of the Q-linear convergence rate under the condition that the mapping is locally Lipschitz continuous. Finally, by applying the Bayesian hyperparameter optimization technique, a series of numerical experiment results demonstrate that the new algorithm has advantages in solving nonlinear monotone equation systems with convex constraints and handling compressed sensing problems. [ABSTRACT FROM AUTHOR]

In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a linearized quadratic penalty method, i.e., we linearize the objective function and the functional constraints in the penalty formulation at the current iterate and add a quadratic regularization, thus yielding a subproblem that is easy to solve, and whose solution is the next iterate. Under a new adaptive regularization parameter choice, we provide convergence guarantees for the iterates of this method to an ϵ first-order optimal solution in O (ϵ - 2.5) iterations. Finally, we show that when the problem data satisfy Kurdyka–Lojasiewicz property, e.g., are semialgebraic, the whole sequence generated by the proposed algorithm converges and we derive improved local convergence rates depending on the KL parameter. We validate the theory and the performance of the proposed algorithm by numerically comparing it with some existing methods from the literature. [ABSTRACT FROM AUTHOR]

When a widespread funding shock hits the banking system, banks may engage in strategic behaviour to deal with funding shortages by a pre-emptive disposal of assets. Alternatively, they may adopt a more cautious strategy to mitigate price reactions, thereby distributing the assets sales into smaller portions over time. We model banks' optimal behaviour using standard optimisation techniques and show that an equilibrium always exits in a stylised setting. A numerical analysis to approximate the equilibrium supplements the theoretical part. The implementation delivers two liquidity measures for the German banking system: the Systemic Liquidity Buffer and the Systemic Liquidity Shortfall. These measures are more informative about systemic liquidity risk than regulatory liquidity measures, such as the LCR, because they model adverse, nonlinear price dynamics in a more realistic way. Our approach is applied to different stress scenarios. [ABSTRACT FROM AUTHOR]

In light of the great development witnessed by our contemporary world, it has become necessary to focus on scientific methods and use the quantitative method to reach more accurate decisions, appropriate to the surrounding circumstances and factors. The process of decision-making and choosing the optimal alternative depends on the type and quality of data that describes the issue for which the decision is to be made. Regarding it, in this chapter we present a study of the issue of determining the ideal advertising medium to display a company's products. This issue is considered one of the issues of decision-making in the case of confirmed data, so we build the appropriate mathematical model and through the optimal solution to it we can make the ideal decision through which the company achieves its goal from the campaign. Informative, we will divide this study into two parts. In the first section, we will develop a general formula for this issue, and the data will be classical values. We will obtain a linear mathematical model. In the second section, we will formulate the issue from the perspective of neutrosophic science, meaning we will take the data as neutrosophic values, obtaining a linear neutrosophic model. [ABSTRACT FROM AUTHOR]

Purpose: Using recent US regional data associated with food system operations, this study aims at building optimization and econometric models to incorporate varying influential factors on food hub location decisions and generate effective facility location solutions. Design/methodology/approach: Mathematical optimization and econometric models have been commonly used to identify hub location decisions, and each is associated with specific strengths to handle uncertainty. This paper develops an optimization model and a hurdle model of the US fresh produce sector to compare the hub location solutions between these two modeling approaches. Findings: Econometric modeling and mathematical optimization are complementary approaches. While there is a divergence between the results of the optimization model and the econometric model, the optimization solution is largely confirmed by the econometric solution. A combination of the results of the two models might lead to improved decision-making. Practical implications: This study suggests a future direction in which model development can move forward, for example, to explore and expose how to make the existing modeling techniques easier to use and more accessible to decision-makers. Social implications: The models and results provide information that is currently limited and is useful to help inform sustainable decisions of various stakeholders interested in the development of regional food systems, regional infrastructure investment and operational strategies for food hubs. Originality/value: This study sheds light on how the application of complementary modeling approaches improves the effectiveness of facility location solutions. This study offers new perspectives on elaborating key features to encompass facility location issues by applying interdisciplinary approaches. [ABSTRACT FROM AUTHOR]