This work tackles the problem of image restoration, a crucial task in many fields of applied sciences, focusing on removing degradation caused by blur and noise during the acquisition process. Drawing inspiration from the multi-penalty approach based on the Uniform Penalty principle introduced in [Bortolotti et al. arXiv.math.NA/2309.14163], we develop here a new image restoration model and an iterative algorithm for its effective solution. The model incorporates pixel-wise regularization terms and establishes a rule for parameters selection, aiming to restore images through the solution of a sequence of constrained optimization problems. To achieve this, we present a modified version of the Newton Projection method, adapted to multi-penalty scenarios, and prove its convergence. Numerical experiments demonstrate the efficacy of the method in eliminating noise and blur while preserving the image edges.

In this paper, we extend the Merton model of investment in discrete time to the cases when there is a finite number of investors and the market is with frictions represented by convex penalty functions defined for each investor. In the main result of this paper, we proved the existence of optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model.

This paper introduces the exponential time differencing (ETD) technique as a numerical method to solve efficiently American vulnerable options pricing. We address several challenges, including removing cross-derivative terms through appropriate transformations, treating early-exercise opportunities using the penalty method, and substituting fixed boundary conditions with corresponding one-sided finite differences. The proposed method is shown to be both accurate and efficient through numerical experiments, which also compare the results with existing methods and analyse the numerical stability and convergence rate.

This paper presents the results of quantitative research regarding the predictive model of citizens' attitudes about the risks of introducing the death penalty in the Republic of Serbia legal system. The research was conducted with the use of a questionnaire that was requested and then collected online from 427 people in June 2021. A multivariate regression analysis was used, identifying the extent to total scores of the main dependent variables (introducing the death penalty; trust in the legal system; advantages of introduction; disadvantages of introduction scores) were associated with five demographic and socio-economic variables: gender, marital, education, income, and age. We tested the central hypothesis of which gender is predicting variables citizens' attitudes about the risks of introducing the death penalty in the legal system of Serbia. The findings revealed that gender and educational level were the most effective predictors of the research variables under question. The majority of respondents support the introduction of the death penalty and the most important predictor of disadvantages of introducing the death penalty in the legal system is age. Based on the findings that there are major differences in the citizens' attitudes about the risks of introducing the death penalty in the legal system, policies, strategies, and regulations must take into account these very important findings.

This paper presents an alternative constraint handling approach within a specialized genetic algorithm (SGA) for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a nonlinear single-objective optimization problem aiming to minimize power losses while keeping network constraints. The proposed constraint handling approach is based on a product of sub-functions that represents permissible limits on system variables and that includes a specific goal on power loss reduction. The main advantage of this approach is the fact that it allows a straightforward verification of both feasibility and optimality. The SGA is examined and tested with the proposed constraint handling approach and the traditional penalization of deviations from feasible solutions. Several tests are run in the IEEE 30, 57, 118 and 300 bus test power systems. The results obtained with the proposed approach are compared to those offered by other metaheuristic techniques reported in the specialized literature. Simulation results indicate that the proposed genetic algorithm with the alternative constraint handling approach yields superior solutions when compared to other recently reported techniques.

This article describes the choice of an optimization algorithm for solving problems and the optimal design of an unmanned aerial vehicle propeller. To solve the problem using evolutionary algorithms, it was transformed into an unconstrained optimization problem using a penalty function. The airfoil contours were constructed using a Bezier curve. Design variables were divided into two types: those that describe in general terms the propeller geometry or operation, such as propeller diameter, number of blades, and rev/min; and those that vary with propeller radius, such as chord length, effective airfoil angle, and airfoil geometry. The objective function is the calculation of the propeller power required to achieve a given thrust. The differential evolution algorithm was used to solve this problem.

Today’s purchasing companies demand an advanced buyer equal of enactment from their supplier while the two parties maintain a respectful connection. Although the supplier selection (SC) product life cycle cost (SCPLCC) is an important consideration among corporations, SCPLCC problem has become associated with deciding how one supplier should be selected from possible alternatives. In this study, we applied two types of goal programming, multiobjective linear programming and revised multichoice goal programming to develop a PLCC-based concept to solve the SCPLCC problem and construct a decision-making tool for application to a case of supply chain management in a Taiwanese light-emitting diode company in the high-tech industry. Our study main contribution Company managers can easily use the two approaches of the SCPLCC model with different parameters to solve SCPLCC model problems. Finally, we comparing five models found RMCGP with weighted linear goal programming had an adequate effect for application to the PLCC concept for high-technology comapny; this cloud make company decision–makers focus on low PLCC and select better supplier.

We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.

Supplier selection (SC) continues to be a crucial component in manufacturing procurement. Using the PLCC advantages generates revenue and lowers costs more than might be anticipated. Supplier selection (SC) product life cycle cost (SCPLCC) is an important consideration among corporations, SCPLCC problem has become associated with deciding how one supplier should be selected from possible alternatives. Past literature on this topic is limited. We try to close this gap in knowledge. In this study, we attempt to apply two types of goal programming, multiobjective linear programming and revised multichoice goal programming to develop a PLCC-based concept to solve the SCPLCC problem and construct a decision-making tool for application to a case of supply chain management in a Taiwanese light-emitting diode company in the high-tech industry. Our study main contribution Company managers can easily use the two approaches of the SCPLCC model with different parameters to solve SCPLCC model problems. Finally, we are comparing five models found RMCGP with weighted linear goal programming had an adequate effect for application to the PLCC concept for high-technology Company; this cloud makes company decision–makers focus on low PLCC and select a better supplier in sustainable supply chains development.

The classical joint economic lot-sizing (JELS) policy in a single-vendor single-buyer system generates an equal production quantity in all cycles, where the input parameters remain static indefinitely. In this paper, a new two-echelon supply chain inventory model is developed involving a hybrid production system that simultaneously focuses on green and regular production methods with optimal allocation fraction of green and regular productions. Unlike the classical mathematical formulation, each cycle is independent from the previous one, and consequently, the input parameters can be adjusted to be responsive to the dynamic nature of demand rate and price fluctuation. A rigorous heuristic approach is used to derive a global optimal solution for a joint hybrid production system. The model accounts for carbon emissions from production and storage activities related to green and regular produced items along with transportation activity under a multi-level emission-taxing scheme. The results emphasize the significant impact of green production on emissions. That is, the higher the allocation fraction of green production the lower the total amount of emissions generated by the system, i.e., the system becoming more sustainable. Adopting a hybrid production method not only decreases the greenhouse gas (GHG) emissions dramatically, but also reduces the per unit time total cost when compared with regular production. One of the main findings is that the total system cost generated by the base closed-form formula of the proposed model is considerably lower than that of the existing literature i.e., 33.59% (16.13%) lower in the first cycle (subsequent cycles) when the regular production method is assumed. Moreover, the optimal production rate generated by the proposed model is the one that minimizes the emissions production function. Illustrative examples and special cases that reflect different realistic situations are compared to outline managerial insights.