Relaxation Approach Research Articles

A relaxation viewpoint to Unbalanced Optimal Transport: Duality, optimality and Monge formulation

We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex envelope of a cost for non-negative Dirac masses. New general primal-dual formulations, optimality conditions, and metric-topological properties are carefully studied and discussed.

Effect of particle size on optical and electrical properties of thin films – a simulation approach

This paper presents a simulated investigation of the relationship between surface roughness and particle size as well as the resulting impact of the both on the thin film’s physical and optical properties. Non-porous thin films are created through computer simulation for a range of particle sizes following the random deposition with a surface relaxation approach. For the deposited thin films different fundamental parameters like transmittance, reflectance, absorption coefficients, frequency dependent dielectric constants, loss angle, refractive indices, optical band gap have all been calculated and in this process of calculation the fundamental values of two different materials; zinc oxide (ZnO and cadmium selenide (CdSe) are taken. It has been seen that when the particle sizes are comparable the calculated values of optical band gap of both ZnO and CdSe matches well with the experimental values of the same reported by others. This is probably the first effort to develop a direct relation between the particle size with different fundamental optical properties of different materials through simple simulation which agrees well with the experimental result. This would definitely help the experimental researchers in the field of material science to design their experiments as per the desired requirements.

Sparse sensor selection for distributed systems: An [formula omitted]-relaxation approach

We study the problem of sensor selection for distributed systems, where a large number of sensors are located spatially in many different locations. Specifically, we consider both perfect and packet-dropping communication channels. While the original problem is NP-hard, by adopting a sparse design, we can solve the problem via convex optimization and reduce the computation cost significantly. Our method not only handles correlated measurement noise but also can be easily extended to actuator selection or sensor-and-actuator (SaA) selection problems. Simulation shows that our sparsity-based approach performs similarly to the brute force optimal strategy while consuming significantly less computation time. Additionally, our method is shown to outperform the state-of-art method notably.

Application of IoT technology for enhancing the consumer willingness to return E-waste for achieving circular economy: A Lagrangian relaxation approach

Poor management of waste electronic and electrical equipment (e-waste) has resulted in serious challenges to the environment and, consequently, to living organisms. Increasing consumer willingness to return household e-waste is a practical solution for better e-waste management. In this paper, for the first time, a circular supply chain network is structured by applying internet of things (IoT) technology to increase consumer willingness to return household e-waste and to manage the network more effectively. For this purpose, we formulate a mixed-integer linear programming model whose objective is to minimize strategic costs (setup costs and IoT deployment costs) and operational costs (transportation costs, costs associated with IoT, and processing costs in centers), simultaneously. In addition, we developed a heuristic algorithm based on Lagrangian relaxation to solve the proposed MILP model. The performance of the proposed algorithm is evaluated by comparing its results with GAMS results using eight small-sized simulated problems. Furthermore, eight large-size problems are simulated and solved by the proposed algorithm. Finally, the data of an Iranian knowledge-based company is employed to validate the presented mathematical model and algorithm, and the sensitivity analysis process is used to examine the accuracy of the obtained results.

A Conic Relaxation Approach for Solving Stackelberg Pricing Game of Electric Vehicle Charging Station Considering Traffic Equilibrium

A Conic Relaxation Approach for Solving Stackelberg Pricing Game of Electric Vehicle Charging Station Considering Traffic Equilibrium

Lp-norm relaxation approach for 3D measurement via instantaneous light field of ethylene premixed flames

Optical imaging technology based on flame spontaneous radiation is a promising tool for combustion diagnosis. However, the existing radiation thermometry technology faces the problems of low angular resolution and low efficiency in solving radiative transfer. Therefore, a novel optical imaging model is proposed, which combines light field imaging theory with equation-solving integral equation method based on radiation distribution factor to effectively decouple the radiative properties related to transfer process and the temperature-related source terms. Aiming at the problem that traditional method may cause over-smooth effect, Lp-norm regularization based on non-negative constraint is established. Results show that Lp-norm can improve reconstruction quality and robustness, but p value needs to be reasonably selected according to noise level and flame inhomogeneity. Experimental study of ethylene/air-premixed flames shows that the methodology can realize 3D measurement (900 ∼ 1550 K). Compared with laser absorption spectroscopy and thermocouple, error is better than 3 % at height above burner 15 mm.

Monolithic and local time-stepping decoupled algorithms for transport problems in fractured porous media

Abstract The objective of this paper is to develop efficient numerical algorithms for the linear advection-diffusion equation in fractured porous media. A reduced fracture model is considered where the fractures are treated as interfaces between subdomains and the interactions between the fractures and the surrounding porous medium are taken into account. The model is discretized by a backward Euler upwind-mixed hybrid finite element method in which the flux variable represents both the advective and diffusive fluxes. The existence, uniqueness, as well as optimal error estimates in both space and time for the fully discrete coupled problem are established. Moreover, to facilitate different time steps in the fracture-interface and the subdomains, global-in-time, nonoverlapping domain decomposition is utilized to derive two implicit iterative solvers for the discrete problem. The first method is based on the time-dependent Steklov–Poincaré operator, while the second one employs the optimized Schwarz waveform relaxation (OSWR) approach with Ventcel-Robin transmission conditions. A discrete space-time interface system is formulated for each method and is solved iteratively with possibly variable time step sizes. The convergence of the OSWR-based method with conforming time grids is also proved. Finally, numerical results in two dimensions are presented to verify the optimal order of convergence of the monolithic solver and to illustrate the performance of the two decoupled schemes with local time-stepping on problems of high Péclet numbers.

The impact of ruminative thought style on the maintenance of depressive mood

Introduction Ruminations are a cognitive style of “thought recycling”, which involves passively and repeatedly focusing on disorder and distress symptoms, or their causes, without attempting to alleviate them. They are a significant indicator of cognitive vulnerability, predicting the emergence, maintenance, and recurrence of depressive symptoms.ObjectivesTo estimate the impact of the ruminative thought style on the maintenance and escalation of depressive mood.Methods The research sample consisted of 60 students between the ages of 19 and 30 (M = 23), divided into two experimental groups with 30 participants each. The participants took part in a 5-minute experiment that involved recalling an autobiographically sad event, assessing their mood on the Scale for Self-Assessment of Emotions (EAS) before and after the induction, and then splitting into two groups of 30 participants for random ruminating or distraction. The Beck Depression Inventory-II, the Ruminative Response Scale, the Ruminative Thought Style Questionnaire, and the EAS were used as research instruments. The progressive group relaxation approach was used at the end of the experiment with all participants to promote relaxation and lessen the psychophysical tension brought on by the experimental induction (10 minutes total).ResultsThe experimental groups did not differ in mood intensity prior to the induction of sadness. Both experimental groups experienced significant impacts on depressed mood following the induction of sadness (F (1,58) =92.05, p<0.001): participants who ruminated demonstrated persistence in their negative mood, whereas participants who engaged in distractions demonstrated a decrease in their negative mood, even below the initial level (F (2,116) =12.69, p<0.001).Conclusions This result provides an additional experimental validation of the phenomenon of maintaining a depressive mood through ruminations. An essential psychotherapy goal should be the treatment (metacognitive therapy, rumination-focused CBT, mindfulness, cognitive bias correction, etc.) of such mechanisms, recognized as crucial for the maintenance of depression.Disclosure of InterestNone Declared

Structural Relaxation Approach to H ∞ Control With Quadratic Fuzzy Lyapunov Function for Continuous-Time Takagi–Sugeno Fuzzy Systems

Structural Relaxation Approach to <i>H</i> _∞ Control With Quadratic Fuzzy Lyapunov Function for Continuous-Time Takagi–Sugeno Fuzzy Systems

A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem

In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.

GaLileo: General Linear Relaxation Framework for Tightening Robustness Certification of Transformers

Transformers based on attention mechanisms exhibit vulnerability to adversarial examples, posing a substantial threat to the security of their applications. Aiming to solve this problem, the concept of robustness certification is introduced to formally ascertain the presence of any adversarial example within a specified region surrounding a given sample. However, prior works have neglected the dependencies among inputs of softmax (the most complex function in attention mechanisms) during linear relaxations. This oversight has consequently led to imprecise certification results. In this work, we introduce GaLileo, a general linear relaxation framework designed to certify the robustness of Transformers. GaLileo effectively surmounts the trade-off between precision and efficiency in robustness certification through our innovative n-dimensional relaxation approach. Notably, our relaxation technique represents a pioneering effort as the first linear relaxation for n-dimensional functions such as softmax. Our novel approach successfully transcends the challenges posed by the curse of dimensionality inherent in linear relaxations, thereby enhancing linear bounds by incorporating input dependencies. Our evaluations encompassed a thorough analysis utilizing the SST and Yelp datasets along with diverse Transformers of different depths and widths. The experimental results demonstrate that, as compared to the baseline method CROWN-BaF, GaLileo achieves up to 3.24 times larger certified radii while requiring similar running times. Additionally, GaLileo successfully attains certification for Transformers' robustness against multi-word lp perturbations, marking a notable accomplishment in this field.

An efficient branch and bound reduction algorithm for globally solving linear fractional programming problems

This paper investigates a class of linear fractional programs (LFP) with linear constraints, which are widely applied in transportation, economic investment and so on. We start with transforming LFP into its equivalent two-layer problem. Subsequently, we introduce a novel linear relaxation approach and integrate it within the branch and bound framework, and a new global optimization algorithm is presented in cooperation with a region deleting rule. Additionally, we discuss the convergence and complexity of this algorithm. Preliminary numerical results validate the practicality and effectiveness of our proposed method.

Learning-based Relaxation of Completeness Requirements for Data Entry Forms

Data entry forms use completeness requirements to specify the fields that are required or optional to fill for collecting necessary information from different types of users. However, because of the evolving nature of software, some required fields may not be applicable for certain types of users anymore. Nevertheless, they may still be incorrectly marked as required in the form; we call such fields obsolete required fields. Since obsolete required fields usually have “not-null” validation checks before submitting the form, users have to enter meaningless values in such fields to complete the form submission. These meaningless values threaten the quality of the filled data and could negatively affect stakeholders or learning-based tools that use the data. To avoid users filling meaningless values, existing techniques usually rely on manually written rules to identify the obsolete required fields and relax their completeness requirements. However, these techniques are ineffective and costly. In this article, we propose LACQUER, a learning-based automated approach for relaxing the completeness requirements of data entry forms. LACQUER builds Bayesian Network models to automatically learn conditions under which users had to fill meaningless values. To improve its learning ability, LACQUER identifies the cases where a required field is only applicable for a small group of users and uses SMOTE, an oversampling technique, to generate more instances on such fields for effectively mining dependencies on them. During the data entry session, LACQUER predicts the completeness requirement of a target based on the already filled fields and their conditional dependencies in the trained model. Our experimental results show that LACQUER can accurately relax the completeness requirements of required fields in data entry forms with precision values ranging between 0.76 and 0.90 on different datasets. LACQUER can prevent users from filling 20% to 64% of meaningless values, with negative predictive values (i.e., the ability to correctly predict a field as “optional”) between 0.72 and 0.91. Furthermore, LACQUER is efficient; it takes at most 839 ms to predict the completeness requirement of an instance.

A relaxation approach to modeling properties of hyperbolic–parabolic type models

In this work, we propose a novel relaxation modeling approach for partial differential equations (PDEs) involving convective and diffusive terms. We reformulate the original convection–diffusion problem as a system of hyperbolic equations coupled with relaxation terms. In contrast to existing literature on relaxation modeling, where the solution of the reformulated problem converges to certain types of equations in the diffusive limit, our formalism treats the augmented problem as a system of coupled hyperbolic equations with relaxation acting on both the convective flux and the source term. Furthermore, we demonstrate that the new system of equations satisfies Liu’s sub-characteristic condition. To verify the robustness of our proposed approach, we perform numerical experiments on various important models, including nonlinear convection–diffusion problems with discontinuous coefficients. The results show the promising potential of our relaxation modeling approach for both pure and applied mathematical sciences, with applications in different models and areas.

Comprehensive Numerical Modeling of Prestressed Girder Bridges under Low-Velocity Impact

Accidental collisions involving over-height trucks that exceed vertical clearance limits and bridge superstructures frequently happen, resulting in compromised girders and potential threats to structural safety and performance. The numerical simulation of large-scale prestressed girder bridge collisions poses challenges due to the associated nonlinearities, as well as the limited availability of large-scale experimental testing data in the literature due to cost and complexity constraints. This study introduces a numerical modeling approach to efficiently capture the response of prestressed girder bridges under lateral impact loads. A finite element (FE) model was developed using LS-DYNA and meticulously validated against experimental data from the literature. The study explored four methods for applying prestressing forces and evaluated the performance of four concrete material constitutive models, including the Continuous Surface Cap Model (CSCM), Concrete Damage Plastic Model (CDPM), Karagozian &amp; Case Concrete (KCC) model, and Winfrith concrete model, under impact loads. Furthermore, an impact study was conducted to investigate the influence of impact speed, impact mass, and prestressing force on the behavior of prestressed girder bridges. Utilizing the dynamic relaxation (DR) approach, the developed FE model precisely captured the response of prestressed girders under impact loads. The CSCM yielded the most accurate predictions of impact forces, with an error of less than 8%, and demonstrated a strong ability to predict damage patterns. Impact speed, mass, and the presence of prestressing force showed a significant influence on the resulting peak impact force experienced by the girder. Furthermore, the study underscores the composite nature of the bridge’s response and emphasizes the importance of analyzing the bridge as a whole rather than focusing solely on individual girders.

A Problem based on Lagrange Relaxation Approach &amp; Solving Optimization on Bi-level Model Programming Problem

Abstract: In this paper, a salutation method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. Linearized taking advantage of the structure of the leading problem, an algorithm is solving two-dimensional bi-level linear programming problems, classification of constrains, algorithm removes all redundant constraints, cycling and solution of problem.

Assessing the need for a deregulation of the insurance sector of Mauritius to combat money laundering: a comparative study with Singapore and UK

PurposeThe purpose of this paper is to assess the current legal framework on money laundering control in the insurance sector. Essentially, this examination is premised on the interrogation of whether it is still appropriate for Mauritius to apply such stringent, opaque and unyielding Anti-Money Laundering/Combating Financing of Terrorism norms and rules on general insurance when developed nations such as the UK and Singapore have done away with them for a more effective combat against money laundering. It would also be assessed why the financial services commission (FSC) is not able to draw inspiration from its British and Singaporean counterparts in fighting money laundering more effectively.Design/methodology/approachThis paper uses the doctrinal legal research methodology which is colloquially described as “black-letter law” approach. It is backed up by a contextual legal analysis that is based on an analysis of relevant legal provisions. It relies ground experience from the insurance industry through the experience of the authors. A comparative approach is used with Singapore and the UK as case studies given that there are significant commonalities to the Mauritian jurisdiction as well as useful differences.FindingsIt is observed that a move towards a de-regulation of the legal framework on money laundering in the insurance sector with a more relaxed approach is more effective for the Mauritian insurance sector. Evidence is drawn from the Singaporean and British models. A re-structuring of the FSC of Mauritius is also warranted for such an approach to be adopted.Originality/valueThis paper is among the first academic contribution that proposes a de-regulation and the adoption of a relaxed approach of and by the Mauritian Insurance Industry for a more effective combat against money laundering. It serves as a legal foundational basis for further research in this direction.

Strength-based topology optimisation of anisotropic continua in a CAD-compatible framework

In this paper, a new method to address strength-based topology optimisation (TO) problems is proposed. Specifically, failure criteria for anisotropic materials are integrated into a TO algorithm making use of Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field describing the topology of the continuum, thus providing solutions that can be easily exported to any computer-aided design software. The notion of failure load factor is introduced to obtain optimised topologies that do not depend on the magnitude of the applied loads. A unified formulation of the main phenomenological criteria for anisotropic materials, i.e., Tsai–Wu, Hoffman and Tsai–Hill criteria, is used and typical issues related to stress-based TO problems, such as local behaviour and singularity of stresses, are handled thanks to: the properties of NURBS blending functions, a special adaptive χ-norm aggregation function that avoids overflow/underflow issues, and a modified pq relaxation approach. The effectiveness of the proposed approach is demonstrated on 2D and 3D problems. A sensitivity analysis of the optimised topologies to the integer parameters involved in the definition of the NURBS entity is performed. Moreover, the influence of the penalisation scheme used for the elasticity and the stress tensors, the failure criterion, and the orientation of the material on the optimal solution is also investigated.

Decentralized robust operation of the unbalanced microgrids in distribution networks: A convex relaxation approach

This work presents a distributed robust operation framework for the microgrids within the power distribution network. It addresses the uncertainties in photovoltaic generation, as well as active, and reactive loads in the network, by modeling them using polyhedral sets. The energy management problems are formulated as two-stage optimization problems in microgrids and power distribution networks for which Benders decomposition is used to solve the problems. The power flow constraints are relaxed using second-order cone relaxation and moment relaxation techniques in the power distribution network and microgrid energy management problems, respectively. The interaction between the microgrids and the power distribution network is represented using the price signal and the exchanged active and reactive power at the microgrids’ points of common coupling. The effectiveness of the proposed framework is shown using two case studies on IEEE 37-bus and IEEE 123-bus systems. The effect of the energy storage system on the operational cost of the system is assessed. It is shown that total operation cost is decreased by 9.69% when the energy storage system is integrated into the power distribution network. Additionally, the solution derived from the robust problem is compared with that of the deterministic problem.

Dynamic prediction of survival using multivariate functional principal component analysis: A strict landmarking approach.

Dynamically predicting patient survival probabilities using longitudinal measurements has become of great importance with routine data collection becoming more common. Many existing models utilize a multi-step landmarking approach for this problem, mostly due to its ease of use and versatility but unfortunately most fail to do so appropriately. In this article we make use of multivariate functional principal component analysis to summarize the available longitudinal information, and employ a Cox proportional hazards model for prediction. Additionally, we consider a centred functional principal component analysis procedure in an attempt to remove the natural variation incurred by the difference in age of the considered subjects. We formalize the difference between a 'relaxed' landmarking approach where only validation data is landmarked and a 'strict' landmarking approach where both the training and validation data are landmarked. We show that a relaxed landmarking approach fails to effectively use the information contained in the longitudinal outcomes, thereby producing substantially worse prediction accuracy than a strict landmarking approach.