Penalty Approach Research Articles

Exact $$l_1$$ exponential penalty approach for interval-valued mathematical problems

Exact $$l_1$$ exponential penalty approach for interval-valued mathematical problems

A Machine Learning Method for Stackelberg Mean Field Games

We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In the Stackelberg MFG, an infinite population of agents plays a noncooperative game and chooses their controls to optimize their individual objectives while interacting with the principal and other agents through the population distribution. The principal can influence the mean field Nash equilibrium at the population level through policies, and she optimizes her own objective, which depends on the population distribution. This leads to a bilevel problem between the principal and mean field of agents that cannot be solved using traditional methods for MFGs. We propose a reformulation of this problem as a single-level mean field optimal control problem through a penalization approach. We prove convergence of the reformulated problem to the original problem. We propose a machine learning method based on (feed-forward and recurrent) neural networks and illustrate it on several examples from the literature. We also give a modified example to show the scalability of the proposed method and show its efficiency by comparing its performance with an alternative bilevel approach.

Enhancing energy efficiency in MC-NOMA systems through optimized channel and power allocation

Non-orthogonal multiple access (NOMA) has quickly become popular due to its higher spectral efficiency (SE) and is crucial in extending future networks’ capacity. This paper presents an innovative approach to enhancing energy efficiency (EE) in downlink (DL) multi-carrier (MC) NOMA systems, in which a single base station (BS) supports a group of users across multiple sub-channels. A novel least user sum gain-based user assignment (LUSGUA) algorithm is proposed in this paper, which prioritizes users with the lowest channel gains for optimal sub-carrier allocation. Additionally, a novel power allocation (PA) scheme is developed across sub-carriers to further improve energy efficiency (EE), throughput, and fairness. throughput and fairness. Since the PA optimization problem (OP) is constrained and non-convex, to tackle this problem, a penalty approach (PTA) is proposed, which is then addressed by particle swarm optimization (PSO) with sequential optimization of the inter/intra-level PA. Power is allocated across sub-carriers at the inter-level using PSO, while at the intra-level, power is distributed among users via the Bisection Method (BM). Simulation results demonstrate that the proposed algorithm achieves significant enhancements in EE, with improvements ranging from 13.04% to 48.67% compared to existing resource allocation (RA) schemes techniques, while also improving system throughput, fairness, and outage percentage. These results highlight substantial advancements over traditional methods.

Flexible modelling of time-varying exposures and recurrent events to analyse training load effects in team sports injuries

Abstract We present a flexible modelling approach to analyse time-varying exposures and recurrent events in team sports injuries. The approach is based on the piece-wise exponential additive mixed model where the effects of past exposures (i.e. high-intensity training loads) may accumulate over time and present complex forms of association. In order to identify a relevant time window at which past exposures have an impact on the current risk, we propose a penalty approach. We conduct a simulation study to evaluate the performance of the proposed model, under different true weight functions and different levels of heterogeneity between recurrent events. Finally, we illustrate the approach with a case study application involving an elite male football team participating in the Spanish LaLiga competition. The cohort includes time-loss injuries and external training load variables tracked by Global Positioning System devices, during the seasons 2017–2018 and 2018–2019.

A unified framework for the error analysis of physics-informed neural networks

Abstract We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity, parabolic, hyperbolic and Stokes equations, and a PDE constrained optimization problem. For the analysis, we propose an abstract framework in the common language of bilinear forms, and we show that coercivity and continuity lead to error estimates. The obtained estimates are sharp and reveal that the $L^{2}$ penalty approach for initial and boundary conditions in the PINN formulation weakens the norm of the error decay. Finally, utilizing recent advances in PINN optimization, we present numerical examples that illustrate the ability of the method to achieve accurate solutions.

Pendekatan Non Penal Dalam Penanggulangan Kekerasan Seksual Verbal Anak

Introduction: Child verbal sexual crimes are still a serious problem and this is a social disaster that worries society. This condition demands the protection of children.Purposes of the Research: This study aims to analyze and discuss whether the non-penal approach is effective in dealing with child verbal sexual violence and what non-penal approaches can be used in tackling child verbal sexual violence.Methods of the Research: The research method used is an empirical juridical research type. The research locations are the Gasira Maluku Foundation, Ambon 1 Public High School, Ambon 4 State Vocational School and the National Commission on Human Rights. Polulation, research samples of Gasira assistant staff, counseling teachers at SMA Negeri 1 Ambon, counseling teachers at SMK Negeri 4 Ambon and Komnas HAM analyst staff. Data collection through observation and interviews. Data processing and data analysis using qualitative methods.Results of the Research: The results of the study show that the non-penal approach is not yet effective in tackling child verbal sexual violence. This is because children's verbal sexual violence still occurs in schools and in society and is considered something that is normal or usually done to children. Even though verbal sexual violence is sexual violence that is carried out in a non-physical form against children, which is related to parts of the child's body and is related to sexual desire, resulting in intimidation, humiliation, humiliation, or embarrassment. Besides that, the lack of knowledge of school children, parents and the community regarding verbal sexual violence because they do not know what forms, impacts and non-penal approaches and penal approaches in dealing with child verbal sexual violence include. Forms of a non-penal approach that can be used in tackling child verbal sexual violence, namely conducting training, outreach to children and providing counseling and social education in order to develop sensitivity and social awareness of the community regarding the impacts that can arise from acts of child verbal sexual violence, the formation of the individual character of a group or community by providing moral education, religious education and handling child verbal sexual violence by the school and in the community through reprimands and advice to perpetrators not to commit violence and assistance to children as victims of verbal sexual violence.

Optimization of Load-transfer Functions for a Large-diameter Pile in Multi-layered Geological Conditions via a Stochastic Search Algorithm

The paper presents the combination of the load transfer method (computational model) and the genetic algorithm (optimization model) for the automated inverse analysis of instrumented pile load tests. The output of this process are the input parameters governing the shape of the load-transfer functions and thus the prediction accuracy when the load-transfer method is used as a design tool for deep foundations. The optimization problem is converted into an unconstrained task by applying the static penalty approach. Two types of measurements are considered in a newly proposed objective function: the load-displacement curve monitored in a pile head and the axial force profiles along a pile derived from strain gauges. Firstly, the local sensitivity analysis via the Design of Experiments is carried out to identify the parameters of the genetic algorithm which significantly influences the rate of convergence during the optimization process. Subsequently, a fully automated inverse analysis of the loading test of the large-diameter bored pile in multilayered geological conditions is presented. The simultaneous combination of two instrumentation sources leads to a stable unique solution with a sufficient match between the prediction and measurements despite a larger number of unknown – optimized variables.

Revisiting the fitting of the Nelson–Siegel and Svensson models

The Nelson–Siegel and the Svensson models are two widely used models for the term structure of interest rates. These models are quite simple and intuitive, but fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, we provide a novel mathematical analysis of the fitting problem based on parametric optimization. We formulate the fitting problem as a separable nonlinear least-squares problem, in which the linear parameters can be eliminated. We provide a thorough discussion on the conditioning of the inner part of the reformulated problem and show that many of the reported difficulties encountered when solving it are inherent to the problem formulation itself and cannot be tackled by choosing a particular optimization algorithm. Our stability analysis provides novel insights that we use to show that some of the ill-conditioning can be avoided, and that a suitably chosen penalty approach can be used to address the remaining ill-conditioning. Numerical results indicate that this approach has the expected impact while being independent of any choice of a particular optimization algorithm. We further establish smoothness properties of the reduced objective function, putting global optimization methods for the reduced problem on a sound mathematical basis.

Smoothing penalty approach for solving second-order cone complementarity problems

Smoothing penalty approach for solving second-order cone complementarity problems

Stress-based topology optimization using maximum entropy basis functions-based meshless method

AbstractThis paper presents volume-constrained stress minimization-based, topology optimization. The maximum entropy (maxent) basis functions-based meshless method for two-dimensional linear elastic structures is explored. This work focuses to test the effectiveness of the meshless method in handling the stress singularities during the topology optimization process. The commonly used moving least square basis functions are replaced with maximum entropy basis functions, as the latter possess weak Kronecker delta property which leads to the finite element method (FEM) like displacement boundary conditions imposition. The maxent basis functions are calculated once at the beginning of the simulation and then used in optimization at every iteration. Young’s modulus for each background cell is interpolated using the modified solid isotropic material with penalization approach. An open source pre-processor CUBIT is used. A comparison of the proposed approach with the FEM is carried out using a diverse set of problems with simple and complex geometries of structured and unstructured discretization, to establish that maxent-based meshless methods perform better in tackling the stress singularities due to its smooth stress field.

The mixed penalty method for the Signorini problem

We investigate two penalty approaches for the Signorini problem in the mixed form. The well-posedness theory has been established for the two mixed penalty problems in both the continuous and discrete sense. For the continuous case, we obtain the error of the penalty for both two approaches. We also study the error estimates of the discrete mixed penalty problems, which depend on the mesh size and the penalty parameter. Based on the two penalty approaches, we design two algorithms and show their convergence. Several numerical experiments are carried out to confirm the theoretical results.

Viabilidad de la despenalización del narcotráfico en Colombia como asunto de política criminal

This paper reviews how different ex-presidents in Colombia have opted for an anti-narcotics position with a regulated penalization approach. Likewise, it is directed towards a progressive and social struggle, oriented towards legal medical treatment. However, the state has not achieved a means of legal control guaranteeing influence so that it can evaluate the feasibility of decriminalizing drug trafficking in Colombia as a matter of criminal policy aimed at reducing the rate of incidence in the commission of crimes related to drug trafficking, the aim of this work. The handling of this situation has a differential factor in regards to other places such as the state of Texas in the United States. This work try’s to identify the reasons that led the legislator to penalize drug trafficking from a direct, structured and documentary observation. Being drug trafficking a destabilizing factor in State institutions and that generates a serious affectation to legal rights such as public health. Thus violating constitutionally protected rights and where Colombia could not fail to comply with acquired international commitments. Finally, the overwhelming history of drug trafficking has been controversially discussed nationally and internationally. But given the consequences, social thinking, and the stigmatization that speaking or being involved in it entails, represents processes that are progressively articulated around behaviors that are mainly of a mafia nature.

In-Plane and Out-of-Plane Bending Vibration Analysis of the Laminated Composite Beams Using Higher-Order Theories

In this paper, higher-order shear deformation theories for a thorough analysis of the in-plane and out-of-plane vibrational characteristics of laminated composite beams have been presented. Through the introduction of new displacement fields and the consideration of rotary inertia and Poisson's effect, the kinetic and potential energies of the beams have been derived. This formulation, displaying significant generality, accommodates arbitrary stacking sequences. Utilizing the finite element method, a new element has been presented for calculating the beam's vibrational characteristics. Featuring three nodes, each with seven degrees of freedom, this higher-order element provides a detailed representation of complex behaviors. Mass and stiffness matrices have been derived using the energy method and apply boundary conditions through the penalty approach. The results exhibit a high degree of consistency and alignment with those obtained from the 3D commercial software ANSYS, validating the accuracy and reliability of the proposed methodology for structural analysis. This comprehensive approach contributes to advancing the understanding and modeling of laminated composite beams in diverse engineering applications. The effects of different parameters on the in-plane and out-of-plane vibration analysis of laminated composite beams have been investigated in detail.

Optimality and KKT conditions for interval valued optimization problems on Hadamard manifolds

Recently, a new type of optimization problems, the so-called interval optimization problems on Hadamard manifolds, is introduced by the authors in Nguyen et al. [Interval optimization problems on Hadamard manifolds. J Nonlinear Convex Anal. 2023;24(11):2489–2511]. In this follow-up, we further offer the algorithmic bricks for these problems. More specifically, we characterize the optimality and KKT conditions for the interval valued optimization problems on Hadamard manifolds. For unconstrained problems, the existence of efficient points and the steepest descent algorithm are investigated. To the contrast, the KKT conditions and exact penalty approach are explored in the ones involving inequality constraints. These results pave the foundations for the solvability of interval valued optimization problems on Hadamard manifolds.

Optimal pipe-sizing design of water distribution networks using modified Rao-II algorithm

ABSTRACT Several evolutionary algorithms (EAs) have been suggested in the last three decades for the least-cost design of water distribution networks (WDNs). EAs generally worked well to identify the global/near-global optimal solutions for small- to moderate-size networks in a reasonable time and computational effort. However, their applications to large-size networks are still challenging due to large computational effort. Recent developments in EAs are towards parameter-less techniques that avoid fine-tuning of case-specific parameters to reduce the computational effort. Further, several self-adaptive penalties and search-space reduction methodologies have been suggested to reduce the computational effort. A fast, efficient, and parameter-less Rao-II algorithm has been used earlier with penalty-based approaches for the optimal design of WDNs. In this study, the application of a Rao-II algorithm is further explored with three self-adaptive penalty approaches to compare the convergence characteristics. The Rao-II algorithm is observed to converge at an infeasible solution in cases that the applied penalty to an infeasible solution is not so substantial to make it inferior to the feasible solutions. Modifications are suggested to improve the Rao-II algorithm, named the modified Rao-II algorithm. The modified Rao-II algorithm with the self-adaptive penalty methods resulted in better solutions than those obtained earlier.

Theoretical considerations of the volume penalization immersed boundary method for turbulent flows

This Letter explores the volume penalization immersed boundary method for turbulent flows from a more physical perspective. The volume penalization approach consists of introducing a penalty source into the governing equations, resulting in a flow akin to a porous medium with low permeability. Although penalizing the turbulent equations conventionally involves adding a similar penalty source as in the original equations, this work reveals an alternative formulation that includes an additional term with physical meaning. The novelty of this Letter is to consider the penalized flow with an additional property, the fluid resistance, establishing a cross correlation with fluctuating velocity for further modeling.

Diagonally quadratic BSDE with oblique reflection and optimal switching

The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence of a solution by providing some delicate a priori estimates. We further obtain the uniqueness by verifying the first component of the solution is indeed the value of a switching problem for quadratic BSDEs. Moreover, we provide an extension for the solvability and apply our results to study a risk-sensitive switching problem for functional stochastic differential equations.

Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control

Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control

Penal Response to Less Serious Drug Distribution Offenses: The Case of Lithuania in the Regional Context

Abstract Drug distribution is considered one of the most serious crimes in general and the most serious drug offense in particular. Drug distribution may cover behavior of very different levels of seriousness, ranging from the social supply of small quantities of illicit drugs in friend circles to international drug trafficking organized by powerful global crime syndicates. The article explores the criminological contexts of less serious drug distribution and penal frameworks of the relevant countries in the Baltic region. The article argues for a more nuanced penal approach to such offenses in the Lithuanian penal law.

Convergence and error estimates of a penalization finite volume method for the compressible Navier–Stokes system

Abstract In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a numerical method domain-related discretization errors, the so-called variational crimes, need to be taken into account. In this paper we apply the penalty approach to control domain-related discretization errors. We embed the physical domain into a large enough cubed domain and study the convergence of a finite volume method for the corresponding domain-penalized problem. We show that numerical solutions of the penalized problem converge to a generalized, the so-called dissipative weak, solution of the original problem. If a strong solution exists, the dissipative weak solution emanating from the same initial data coincides with the strong solution. In this case, we apply a novel tool of the relative energy and derive the error estimates between the numerical solution and the strong solution. Extensive numerical experiments that confirm theoretical results are presented.