Dual Problem Research Articles

Jacobi method for dual quaternion Hermitian eigenvalue problems and applications

Jacobi method for dual quaternion Hermitian eigenvalue problems and applications

Optimal randomized algorithms of weakly-balanced multi-branching AND-OR trees

This article treats AND-OR tree computation in terms of query complexity. We are interested in the cases where assignments (inputs) or algorithms are randomized. For the former case, it is known that there is a unique randomized assignment achieving the distributional complexity of balanced trees. On the other hand, the dual problem has the opposite result; the optimal randomized algorithms for balanced trees are not unique. We extend the latter study on randomized algorithms to weakly-balanced trees, and see that the uniqueness still fails.

Кількісне оцінювання функціональної ефективності мережевих структур за аналізом чутливості оптимізаційної моделі до зовнішніх впливів

The real network organizational structure is constantly under the influence of external influences, which can cause unexpected consequences due to the cascading spread of relevant disturbances directed at critically important parameters. Parametric sensitivity analysis is the latest computational procedure, the results of which provide the researcher with an idea and quantitative assessment of the appropriate response of the structure in the form of an analytical platform as a composition and interaction of scenario analysis, cascade process development and optimization modeling technology. The main task is timely adaptation to expected changes in business analytics, oriented to optimal resources distribution. The generalized minimum cost problem is a typical example of widespread problems of optimal distribution and use of limited, in particular, energy resources, of any nature and purpose, using the scientific management and analysis of decisions, in its network model attention is paid to the potentials of nodes. The maximum flow problem is an example of the active and effective application of methods and models of flows optimization, where the processes and objects used a network organization, the energy systems and complexes investigated, where arc parameters are critical in its model. In the article, for these classic optimization problems, mathematical and spreadsheet models were built on concrete examples. Direct and dual mathematical programming problems were solved, the following stages were carried out - the organization of a computer experiment and the construction of an analytical platform for evaluating the behavior of the network structure under the influence of external influences and disturbances as their consequences. To take into account the specific conditions of real objects with a network structure at the stage of modification, the model supplemented with appropriate restrictions and correction of input data sets. The obtained results should be useful for planning and management personnel and top-management for discussion and decision-making regarding, for example, the optimal placement of energy equipment, the weighted distribution of energy flows in the "source-sink" system or the appointment of executors for work, automated project management using project networks, etc. Keywords: optimization modeling, maximum network flow, minimum cost flows, network organizational structures, decision making, spreadsheet modeling and analytics.

A POD based extrapolation DG time stepping space-time FE method for parabolic problems

Based on the proper orthogonal decomposition technique, a new reduced-order discontinuous time stepping space-time finite element extrapolation iterative scheme is constructed to solve two-dimensional parabolic problems, which includes very few degrees of freedom but holds sufficiently high accuracy. A reduced space-time projection operator is defined, and its related error estimations are discussed. Then, the error estimate between the classical scheme solution and the reduced-basis scheme solution, and the a priori error estimate for the reduced-basis scheme are derived, respectively. These error estimates are analyzed by using the technique of combining Radau quadrature rule with finite element method, without considering any dual problems. The algorithm implementation of the reduced-order extrapolation iterative scheme is also provided. Finally, a numerical example is presented. The numerical results are consistent with theoretical ones. Moreover, it is shown that the new reduced-order extrapolation iterative scheme, by comparing to the standard approach, can reduce CPU time without loss of accuracy. Therefore, it is feasible and efficient for solving parabolic problems.

Large deformation of cable networks with fiber sliding as a second-order cone programming

A new model for irreversible large deformations of fiber networks is developed. The fibers are considered as inextensible cables that slide relative to each other in the frictional junctions. This sliding is constituted by a rate-independent flow rule. The nonsmooth dissipation potential for each sliding system is defined as a product of the yield strength and the absolute value of the fiber sliding. The response of the cable segments is nonsmooth as well, since it shows asymmetry with respect to tension and compression. A principle of minimum incremental potential and a pure complementary energy principle are derived for the equilibrium incremental loading of the network at large deformations. They form a pair of primal and dual second-order cone programming problems with matching sets of displacement-based and force-based variables. These problems can be effectively solved by interior point methods that have many advantages compared to the gradient-based methods or dynamic relaxation. The model is extended by a simple mechanism of fiber pull-out resulting from fiber sliding at the free unconstrained ends. This can be used for the microstructural analysis of failure of needle-punched nonwoven materials.

Optimizing the Model-prediction of Date Palm Fronds-Derived Producer Gas and Third Generation Biodiesel Powered Dual-fuel engine by Employing Bayesian-Optimized Boosted Regression Trees for Enhanced Prognostics

The global issue concerning the dual problem of economic energy shortage as well as greenhouse gas emission needs urgent attention. Due to its abundance and carbon neutrality, waste biomass is a good energy conversion feedstock. This research suggests a unique method for using date palm frond waste biomass-derived producer gas and algal biodiesel as sustainable diesel engine fuels. The Bayesian-optimized neural networks and Bayesian-optimized Boosted Regression Trees were employed to optimize engine combustion and emission performance. This was further enhanced with the application of k-cross fold to prevent the model from overfitting during training. The working of dual-fuel engines is a complex phenomenon owing to the employment of two different types of fuel one is liquid (biodiesel + diesel) while the other one is gaseous (Producer gas). The present endeavor was undertaken to handle this with the application of advanced data learning methods. The engine was tested at different compression ratios, engine loads, and fuel injection pressures for brake thermal efficiency, diesel fuel substitution, and emission. Both the Bayesian-optimized neural networks and Bayesian-optimized Boosted Regression Trees could predict the engine output with good prediction efficiency with comparable performance, however, the Bayesian-optimized Boosted Regression Trees-based models were more robust with a coefficient of determination value in the range of 0.9617 to 0.9999 and mean squared errors as low as 0.001. The mean absolute percentage error was very low in the range of 0.0316 to 5.231. The Theil’s U2 values were in the range of 0.0029 to 0.0126.

Mahalanobis balancing: A multivariate perspective on approximate covariate balancing

AbstractIn the past decade, various exact balancing‐based weighting methods were introduced to the causal inference literature. It eliminates covariate imbalance by imposing balancing constraints in a certain optimization problem, which can nevertheless be infeasible when there is bad overlap between the covariate distributions in the treated and control groups or when the covariates are high dimensional. Recently, approximate balancing was proposed as an alternative balancing framework. It resolves the feasibility issue by using inequality moment constraints instead. However, it can be difficult to select the threshold parameters. Moreover, moment constraints may not fully capture the discrepancy of covariate distributions. In this paper, we propose Mahalanobis balancing to approximately balance covariate distributions from a multivariate perspective. We use a quadratic constraint to control overall imbalance with a single threshold parameter, which can be tuned by a simple selection procedure. We show that the dual problem of Mahalanobis balancing is an norm‐based regularized regression problem, and establish interesting connection to propensity score models. We derive asymptotic properties, discuss the high‐dimensional scenario, and make extensive numerical comparisons with existing balancing methods.

Stabilization of coupled delayed nonlinear time fractional reaction diffusion systems using sampled‐in‐space sensing and actuation

AbstractThis paper is considered with the asymptotic stabilization of coupled delayed nonlinear time fractional reaction diffusion systems (FRDSs) governed by fractional parabolic partial differential equations (PDEs) with space‐dependent coefficients under sampled‐data in space control. It is assumed that state measurements can be averaged measurements (AMs) or point measurements (PMs), and a finite number of sensing and actuation devices are located in a spaced manner along the spatial domain of the interest. With the proposed sampled‐data in space controller, the closed‐loop stability is obtained. Tuning rules of system parameters and control parameters are derived using the fractional Halanay's inequality and the fractional Lyapunov method. Subsequently, the dual problem of observer design is formulated. Fractional examples are used to valid the theoretical result. Discussions on the extension of sampled‐data boundary feedback stabilization are provided finally.

An approach to duality via image space analysis and applications to linear vector optimization problems

In Yao et al. [Yao CL, Wang SQ, Tammer C. Construction of vector-valued weak separation functions with applications to conjugate duality in vector optimization; 2024. Submitted.], based on the idea of image space analysis and abstract convexity, we proposed a uniform framework of conjugate duality for the constrained vector optimization problems. This paper aims to apply this framework to linear vector optimizations. With the aid of a special collection of separation functions, a set-valued dual problem, which was also derived by Heyde, Löhne, Tammer in [Heyde F, Löhne A, Tammer C. The attainment of the solution of the dual program in vertices for vectorial linear programs. In: Barichard V, Ehrgott M, Gandibleux X, T'Kindt V, editors. Multiobjective programming and goal programming. 2009. p. 13–24. (Lecture Notes in Economics and Mathematical Systems; 618).; Heyde F, Löhne A, Tammer C. Set-valued duality theory for multiple objective linear programs and application to mathematical finance. Math Meth Oper Res. 2009;69:159–179.], is obtained by this approach. Within the uniform framework, we provide a new way to construct this dual model, and to investigate the duality theory of it. In this method, the strong duality is established by the separation of sets in the image space and the generalized saddle points.

Calculation of second-order bearing capacity of members subjected to axial load and biaxial bending

The second-order effects of biaxial bending members involve dual non-linear problems, namely material nonlinearity and geometric nonlinearity. These problems typically require iterative calculations and cannot be solved manually. To address this issue, this paper founded upon the strain-based resolution of stress and internal forces, deduces the formula for calculating the load-bearing capacity of the cross-section. The elastoplastic second-order deformation is then calculated at the member level, and the final result is presented in the form of a dimensionless nomogram for calculating the second-order biaxial bending members. In this paper, the limit range of section strain is determined based on the constitutive relationship of concrete and reinforcement. This range is divided into three limited strain areas, which enable the calculation of section bearing capacity and limit curvature, and subsequently the second-order bearing capacity of the member. The results are in good agreement with experimental data. The dimensionless nomogram in this paper considers the complete parabolic and rectangular of concrete stress-strain relationship and the ideal elastoplastic constitutive relationship of reinforcement and the second-order effect. It does not require iteration. It can quickly calculate the reinforcement or check the section bearing capacity by hand. It can be used to check the calculation results of engineering software and provides ideas for the design method of member subjected to axial load and biaxial bending based on seismic restoring force.

Identification of the surface heat flux of charring ablative materials using dynamic Bayesian network based on multisource information fusion

In order to solve the dual uncertainty problem between heat flux and thermophysical properties in the identification of the heat flux of charring ablative materials, a dynamic Bayesian network (DBN) based on multisource information fusion is proposed. The method is divided into two stages, with thermophysical properties identified in the former stage and the heat flux identified in the latter stage. A one-dimensional pyrolysis layer model is adopted to characterize the ablation process of materials. In the DBN, the multisource information of surface recession and temperature history data are considered as observation nodes. Sensitivity analysis is used to determine the key parameters in each time step in the DBN, and only key parameters are identified in the corresponding time step. Thus, with the increase of types of information and the decrease of the number of simultaneous identification parameters, the identification accuracy can be improved. The method was verified by numerical and experimental cases. In the numerical cases with noise and experimental cases, the maximum error of using the proposed method was 3.27% and 2.55%, respectively. Compared with only considering the temperature information, the relative errors of the identification results considering multisource information fusion were reduced by 83.95% and 47.53%, respectively.

Choosing Optimal Supply Radius of Transformer Substations (TSs) in Iraq’s Cities Using Geometric Programming with Neutrosophic Coefficients

Numerous uncertainties exist in various electricity power system problems due to the size, complexity, geographical distribution, and influence of unforeseen events in these systems, making it difficult for traditional mathematics tools based on crisp set theory to have an impact on and solve many power system problems. As a new branch of mathematical uncertainty techniques, the neutrosophic expert systems approach has therefore emerged with the development of electric power systems and has proven successful when correctly linked. The expert typically uses ambiguous or neutrosophic language to describe their empirical knowledge, such as "very likely," "quite likely," "if x is large, then y is very likely to occur," "x should not be less than a," etc. To design an optimal radius of power supply in the electrical transformer substation, this article presents a new method for creating primal and dual neutrosophic geometric programming problems. It also provides a numerical example to evaluate the approximate optimal economic power supply radius.

SOLAR WIRELESS DYNAMIC ELECTRIC VEHICLE CHARGING SYSTEM

This paper details the making plans and design of a The Solar Wireless Dynamic Electric Vehicle Charging System, a solution to the dual problems of costly gasoline and dangerous emissions. The range of countries with electric cars on the road is gradually rising. In addition to assisting the surroundings, electric cars have validated useful in reducing down on transportation fees by means of substituting highly-priced gas with much greater less costly strength. Here, we create a novel and powerful solution to this problem by means of designing an electric powered vehicle dynamic charging infrastructure. There is no need to stop the car for charging due to the fact the EV can achieve this whilst it's far in movement, the device is powered with the The Solar Wireless Dynamic Electric Vehicle Charging System solar energy and there is no want for an additional power source. Key Words: Solar energy, Solar cell, Arduino Uno controller, Wireless charging, Electric vehicle, Dynamic charging.

The stability and statistic of domain decomposition algorithm with mini-batch learning for optimal transport

The Wasserstein distance in the optimal transport (OT) model is being widely used in machine learning applications due to its mathematical and geometric properties. Since the entropic regularization OT is a convex problem, and for its large-scale problems, many algorithms have been proposed. Existing methods mainly adopt iterative random projection techniques to approximate the Wasserstein distance in the OT model. In this paper, we employ the entropic domain decomposition algorithm with mini-batch learning to calculate the entropic regularization OT problem and investigate the stability of this algorithm. The algorithm performs on different cells of the domain instead of using the projection technique and it is based on a mini-batch loss function. The corresponding solution in each iteration is derived from the dual problem of entropic regularized OT on each decomposed cell. Once the solutions to the dual problem on all decomposed cells are obtained, the corresponding transport plan in each iteration can be obtained. We show that the transport plan computed by its dual variables is admissible, and we also give the sub-gradient approximation result. In addition, we exploit the statistical concentration result of the subsampled mini-batch Wasserstein distance on decomposed cells. Finally, the numerical experiments validate that the proposed algorithm can save computational time further.

On parametric semidefinite programming with unknown boundaries

In this paper, we study parametric semidefinite programs (SDPs) where the solution space of both the primal and dual problems change simultaneously. Given a bounded set, we aim to find the a priori unknown maximal permissible perturbation set within it where the semidefinite program problem has a unique optimum and is analytic with respect to the parameters. Our approach reformulates the parametric SDP as a system of partial differential equations (PDEs) where this maximal analytical permissible set (MAPS) is the set on which the system of PDEs is well-posed. A sweeping Euler scheme is developed to approximate this a priori unknown perturbation set. We prove local and global error bounds for this second-order sweeping Euler scheme and demonstrate the method in comparison to existing SDP solvers and its performance on several two-parameter and three-parameter SDPs for which the MAPS can be visualized.

MTKSVCR: A novel multi-task multi-class support vector machine with safe acceleration rule

Regularized multi-task learning (RMTL) has shown good performance in tackling multi-task binary problems. Although RMTL can be used to handle multi-class problems based on “one-versus-one” and “one-versus-rest” techniques, the information of the samples is not fully utilized and the class imbalance problem occurs. Motivated by the regularization technique in RMTL, we propose an original multi-task multi-class model termed MTKSVCR based on “one-versus-one-versus-rest” strategy to achieve better testing accuracy. Due to the utilization of the idea of RMTL, the related information included in multiple tasks is mined by setting different penalty parameters before task-common and task-specific regularization terms. However, the proposed MTKSVCR is time-consuming since it employs all samples in each optimization problem. Therefore, a multi-parameter safe acceleration rule termed SA is further presented to reduce the time consumption. It identifies and deletes most of the superfluous samples corresponding to 0 elements in the dual optimal solution before solving. Then, only a reduced dual problem is to be solved and the computational efficiency is improved accordingly. The biggest advantage of the proposed SA lies in safety. Namely, it derives an identical optimal solution to the primal problem without SA. In addition, our method remains effective when multiple parameters change simultaneously. Experiments on different artificial datasets and benchmark datasets verify the validity of the proposed methods.

Dynamic asset allocation and consumption ratcheting with costs

This paper delves into studying the optimal decisions regarding consumption and investment for an agent operating within a finite time frame, where any reduction in consumption is intolerable. In contrast to Jeon et al. (2018), we assume that the agent incurs a proportional utility cost with each increase in consumption. To tackle this problem, we employ the duality method to define the dual problem and investigate the resulting upper obstacle problem using PDE techniques. Our study reveals the existence of a critical time attributed to the utility cost, beyond which not only does the agent cease to further increase their consumption, but they also abstain from investing in the risky asset. Furthermore, the existence of the critical time makes free boundary analysis even more challenging, as this is because the presence of the critical time can also lead to the disruption of the monotonicity of the free boundary.

Ohio START: An adaption of the National Sobriety Treatment and Recovery Teams model

BackgroundThe Sobriety Treatment and Recovery Teams (START) model is an evidence-supported intervention for families with at least one child under age 6 involved in the child welfare system due to substance misuse. The hallmark of the START model is early identification and linkage to addiction treatment services. To address the dual problem of heightened need for addiction treatment services and limited treatment availability in the wake of the opioid epidemic, Ohio’s adaptation extended the model to serve all eligible families regardless of the age of children in the household. ObjectiveTo investigate the delivery of the START model for parents and caregivers of older youth (age 6–18) only as compared to the population for which it was originally intended. MethodsWe used data from 40 counties and with parents as the unit of analysis (N = 714). We used multilevel models to estimate the relationship between the age of children in the home and 1) meeting fidelity for timely access to treatment services and 2) successful completion of the model. ResultsThere was no statistically significant difference in the likelihood of meeting fidelity requirement for timely access to treatment services, nor in successful completion for families with older children as compared to those with at least one child aged 0–5. ConclusionsThese results lend support to the use of the START model for all eligible families, regardless of the children’s ages. Future studies can examine more nuanced relationships to include the role of specific substances, child placement, and the role of family peer mentors.

Error estimates for finite element approximations of viscoelastic dynamics: The generalized Maxwell model

We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in L2 norm. The proof is based on an error representation formula using a discrete dual problem and a stability estimate involving the kinetic, elastic, and viscoelastic energies. To set up the dual error analysis and to prove the basic stability estimates, it is natural to formulate the problem as a first-order-in-time system involving evolution equations for the viscoelastic stress, the displacements, and the velocities. The equations for the viscoelastic stress can, however, be solved analytically in terms of the deviatoric strain velocity, and therefore, the viscoelastic stress can be eliminated from the system, resulting in a system for displacements and velocities.

Hybridization in meta-heuristic techniques for green layout design in the tyre manufacturing industry: An optimal analysis

To stop or lessen factory pollution, many academics in the field of study have produced a vast array of strategies to achieve optimization goals. But, it is unable to follow a uniform solution for all production facilities. In this research work, green layout design (GLD) is proposed to minimize total material handling cost (TMHC) and CO2 emissions. The green facility layout refers to the facility layout with minimum CO2 emissions and to eliminate unnecessary energy dissipation from material handling equipments & production machineries, as well as plant re-layout in-term on material handling cost. In this study context, a Lagrangian relaxation model has been used at the allocation level. It computes a suboptimal solution to the dual problem in order to obtain a feasible solution. This enhanced algorithm method iteratively tries to minimize the gap between the dual and feasible solutions on minimal of TMHC and CO2 emission rate. It has been experimentally simulated using the MATLAB (Matrix Laboratory) application and upgraded adaptive salp swarm optimization (ASSO), dragon fly optimization (DFO) and Hybrid (combination) of ASSO-DFO evolutionary optimization techniques. The primary focus of this implementation is to control material handling between departments or cells, production flow between departments, energy consumption (electrical and gas consumption for production), and manpower utilization within and across departments. This research has chosen an existing and acceptable designs from targeted tyre manufacturing company in South India. The hybrid ASSO-DFO implementation TMHC differs from ABC by 60%, DFO by 65%, 58% with simulated annealing (SA), and ASSO by 48%. Emission rate decreased by 26% ABC, 21% DFO, and 24% SA & 18% with ASSO. An average of 50% decrease in TMHC and 25% reduction of CO2 emission rate in GLD have been achieved.