Penalty Technique Research Articles

Projected gradient descent method for cardinality-constrained portfolio optimization

Cardinality-constrained portfolio optimization aims at determining the investment weights on given assets using the historical data. This problem typically requires three constraints, namely, capital budget, long–only, and sparsity. The sparsity restraint allows investment managers to select a small number of stocks from the given assets. Most existing approaches exploit the penalty technique to handle the sparsity constraint. Therefore, they require tweaking the associated regularization parameter to obtain the desired cardinality level, which is time-consuming. This paper formulates the sparse portfolio design as a cardinality-constrained nonconvex optimization problem, where the sparsity constraint is modeled as a bounded ℓ0-norm. The projected gradient descent (PGD) method is then utilized to deal with the resultant problem. Different from existing algorithms, the suggested approach, called ℓ0-PGD, can explicitly control the cardinality level. In addition, its convergence is established. Specifically, the ℓ0-PGD guarantees that the objective function value converges, and the variable sequences converges to a local minimum. To remedy the weaknesses of gradient descent, the momentum technique is exploited to enhance the performance of the ℓ0-PGD, yielding ℓ0-PMGD. Numerical results on four real-world datasets, viz. NASDAQ 100, S&P 500, Russell 1000, and Russell 2000 exhibit the superiority of the ℓ0-PGD and ℓ0-PMGD over existing algorithms in terms of mean return and Sharpe ratio.

A smoothing approximation-based adaptive neurodynamic approach for nonsmooth resource allocation problem

In this paper, a smoothing approximation-based adaptive neurodynamic approach is proposed for a nonsmooth resource allocation problem (NRAP) with multiple constraints. The smoothing approximation method is combined with multi-agent systems to avoid the introduction of set-valued subgradient terms, thereby facilitating the practical implementation of the neurodynamic approach. In addition, using the adaptive penalty technique, private inequality constraints are processed, which eliminates the need for additional quantitative estimation of penalty parameters and significantly reduces the computational cost. Moreover, to reduce the impact of smoothing approximation on the convergence of the neurodynamic approach, time-varying control parameters are introduced. Due to the parallel computing characteristics of multi-agent systems, the neurodynamic approach proposed in this paper is completely distributed. Theoretical proof shows that the state solution of the neurodynamic approach converges to the optimal solution of NRAP. Finally, two application examples are used to validate the feasibility of the neurodynamic approach.

Optimization and heat transfer analysis for MHD radiative natural convective flow of hybrid nanofluid within a partially heated cavity

The current study consists of optimization and heat transfer analysis for magnetohydrodynamic (MHD) radiative-natural convective flow of hybrid nanofluid (mixture of silver and copper nanoparticles with ethylene glycol (base fluid)) saturated inside the partially heated isosceles triangular cavity. Additionally, the current analysis investigates the distraction of available energy during thermal mixing and flow friction through local entropy generation. The conservation laws of total mass, momentum, and energy balance equations have been utilized to govern the physical flow problem. After eradicating the pressure terms in the governing partial differential equations (PDEs) via the penalty technique, the Galerkin finite element method (FEM) with the Newton-Raphson technique has been utilized to solve it. The outcomes established that the concentration of silver nanoparticles, as compared to copper nanoparticles, gives better energy transport. An increase in the concentration of nano-particles from ( ϕ 1 = ϕ 2 = 0 ) to ( ϕ 1 = ϕ 2 = 0.1 ) increased the intensity of streamlines from ψ max = 1.5 to ψ max = 4 and energy transmit rate increases by 57.4 % . The influence of thermal radiation decreased the fluid flow friction or local entropy via fluid flow.

Sparse recovery under nonnegativity and sum-to-one constraints

Sparse recovery under nonnegativity and sum-to-one constraints is a special form of the linear regression problem, where the solution is required to simultaneously satisfy sparsity, nonnegativity, and sum-to-one restraints. Existing algorithms for this task mainly utilize the penalty technique to convert the sparsity constraint into a regularization term. Therefore, the sparsity is determined via tuning the associated penalty parameter, which is time-consuming in practice. This paper exploits projected gradient descent to directly tackle the constrained problem without involving the penalty parameter and ℓ0-norm approximation. The addition of the ℓ0-norm constraint with a specific upper bound enables the proposed algorithm to explicitly control sparsity. The developed method is termed as modified iterative hard thresholding (MIHT), comprised of two iterative steps, namely, gradient descent and nonconvex projection. For the latter, the constraint set consists of the ℓ0-norm, nonnegativity, and sum-to-one constraints. We devise an efficient algorithm to address the nonconvex projection and then prove that this method produces an optimal solution. Furthermore, we establish the convergence of the MIHT, including objective value and variable sequence. Numerical experiments using financial and hyperspectral data demonstrate that the MIHT is superior to state-of-the-art methods in terms of prediction error and recovery accuracy.

Advancing Glaucoma Diagnosis: Employing Confidence-Calibrated Label Smoothing Loss for Model Calibration

ObjectiveThe aim of our research is to enhance the calibration of machine learning models for glaucoma classification through a specialized loss function named Confidence-Calibrated Label Smoothing Loss (CC-LS). This approach is specifically designed to refine model calibration without compromising accuracy by integrating label smoothing and confidence penalty techniques, tailored to the specifics of glaucoma detection. DesignThis study focuses on the development and evaluation of a calibrated deep learning model. ParticipantsThe study employs fundus images from both external datasets-ORIGA (482 normal, 168 glaucoma) and REFUGE (720 normal, 80 glaucoma)-and an extensive internal dataset (4,639 images per category), aiming to bolster the model's generalizability. The model's clinical performance is validated using a comprehensive test set (47,913 normal, 1,629 glaucoma) from the internal dataset. MethodsThe CC-LS loss function seamlessly integrates label smoothing, which tempers extreme predictions to avoid overfitting, with confidence-based penalties. These penalties deter the model from expressing undue confidence in incorrect classifications. Our study aims at training models using the CC-LS and comparing their performance with those trained using conventional loss functions. Main Outcome MeasuresThe model's precision is evaluated using metrics like the Brier score, sensitivity, specificity, and the false positive rate, alongside qualitative heatmap analyses for a holistic accuracy assessment. ResultsPreliminary findings reveal that models employing the CC-LS mechanism exhibit superior calibration metrics, as evidenced by a Brier score of 0.098, along with notable accuracy measures: sensitivity of 81%, specificity of 80%, and weighted accuracy of 80%. Importantly, these enhancements in calibration are achieved without sacrificing classification accuracy. ConclusionsThe Confidence-Calibrated Label Smoothing Loss presents a significant advancement in the pursuit of deploying machine learning models for glaucoma diagnosis. By improving calibration, the CC-LS ensures that clinicians can interpret and trust the predictive probabilities, making AI-driven diagnostic tools more clinically viable. From a clinical standpoint, this heightened trust and interpretability can potentially lead to more timely and appropriate interventions, thereby optimizing patient outcomes and safety.

Research on Parkinson's disease recognition algorithm based on sample enhancement

Parkinson's disease patients have early vocal cord damage, and their voiceprint characteristics differ significantly from those of healthy individuals, which can be used to identify Parkinson's disease. However, the samples of the voiceprint dataset of Parkinson's disease patients are insufficient, so this paper proposes a double self-attention deep convolutional generative adversarial network model for sample enhancement to generate high-resolution spectrograms, based on which deep learning is used to recognize Parkinson's disease. This model improves the texture clarity of samples by increasing network depth and combining gradient penalty and spectral normalization techniques, and a family of pure convolutional neural networks (ConvNeXt) classification network based on Transfer learning is constructed to extract voiceprint features and classify them, which improves the accuracy of Parkinson's disease recognition. The validation experiments of the effectiveness of this paper's algorithm are carried out on the Parkinson's disease speech dataset. Compared with the pre-sample enhancement, the clarity of the samples generated by the proposed model in this paper as well as the Fréchet inception distance (FID) are improved, and the network model in this paper is able to achieve an accuracy of 98.8%. The results of this paper show that the Parkinson's disease recognition algorithm based on double self-attention deep convolutional generative adversarial network sample enhancement can accurately distinguish between healthy individuals and Parkinson's disease patients, which helps to solve the problem of insufficient samples for early recognition of voiceprint data in Parkinson's disease. In summary, the method effectively improves the classification accuracy of small-sample Parkinson's disease speech dataset and provides an effective solution idea for early Parkinson's disease speech diagnosis.

Improvement of Network Reliability by Hybridization of the Penalty Technique Based on Metaheuristic Algorithms

In this study, a network created by converting the Petri net into a network for shutdown system, by calculatinga network’s nonlinear reliability polynomial by splitting the network into two, each having a source node and anterminal node. This the procedure converts the system into two parallel-series block diagrams that are connected ina series. The metaheuristic algorithm using the honey badger algorithm (HBA) and Dwarf Mongoose OptimizationAlgorithm (DMO) have been used to improve the problem for the shutdown network hybridizing these algorithmsemploying the penalty method, we will obtained the (PFMHBA, PFMDMO) algorithms. Thereafter, we comparedthe results of the use of the hybridization technique with the results of the process that does not use this technique. Theobjective of this comparison was to ascertain whether the use of hybridization makes the results increasing reliable,reducing cost, and shortening the duration of implementation.

A Two-Player Resource-Sharing Game with Asymmetric Information

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an ϵ-approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique.

Simulation of flexural-gravity wave propagation for elastic plates in shallow water using an energy-stable finite difference method with weakly enforced boundary and interface conditions

We introduce an energy stable, high-order-accurate finite difference approximation of the dynamic, pure bending Kirchhoff plate equations for complex geometries and spatially variable properties. We utilize the summation-by-parts (SBP) framework to discretize the biharmonic operator with variable coefficients, with attention given to free and clamped boundary conditions and corner conditions. Energy conservation is established by combining SBP boundary closures with weak enforcement of the boundary and interface conditions using a penalty (simultaneous approximation term, SAT) technique. Then we couple the plate equations to the shallow water equations to study flexural-gravity wave propagation, and prove that the semi-discrete system of equations is self-adjoint. We demonstrate the stability and accuracy properties of the method on curvilinear multiblock grids using the method of manufactured solutions. The method, which we provide in an open-source code, is then used to model ocean wave interactions with the Thwaites Glacier and Pine Island Ice Shelf in the Amundsen Sea off the coast of West Antarctica.

Regularised Volterra series models for modelling of nonlinear self-excited forces on bridge decks

Volterra series models are considered an attractive approach for modelling nonlinear aerodynamic forces for bridge decks since they extend the convolution integral to higher dimensions. Optimal identification of nonlinear systems is a challenging task since there are typically many unknown variables that need to be determined, and it is vital to avoid overfitting. Several methods exist for identifying Volterra kernels from experimental data, but a large class of them put restrictions on the system inputs, making them infeasible for section model tests of bridge decks. A least-squares identification method does not restrict the inputs, but the identified model often struggles with noisy (non-smooth) kernels, which is deemed to be unphysical and a sign of overfitting. In this work, regularised least-squares identification is introduced to improve the performance of model identification using least-squares. Standard Tikhonov regularisation and other penalty techniques that impose decaying kernels are also explored. The performance of the methodology is studied using experimental data from wind tunnel tests of a twin deck section. The regularised Volterra models show equal or better results in terms of modelling the self-excited forces, and the regularisation makes the models less prone to overfitting.

The Multi-Objective Transportation Problem Solve with Geometric Mean and Penalty Methods

The traditional (classical) Transportation Problem (TP) can be viewed as a specific case of the Linear Programming (LP) problem, as well as its models are used to find the best solution for the problem of predetermined how many units of a good or service need to be shipped from one source to multiple locations, with the goals being to reduce time or expense. Classical TP has one objective but when there are two or more objectives to be optimized for in a TP, the strategies used to optimize a single objective are inapplicable. The term “Multi-Objective Transportation Problem (MOTP)” refers to situations in which there are two or more objectives in a TP. The specific extension of the transportation problem is the MOTP. This work provided a novel alternative algorithm that uses geometric means along with the penalty technique to address MOTP. Specifically, analyzed data by comparing our method with numerical examples and presenting the results in a line graph. Our analysis shows that our approach yields better solutions than existing methods, demonstrating the novelty and effectiveness of our approach. The comparison with numerical examples provides a clear and intuitive way of presenting the superiority of our method, making it accessible to practitioners and researchers in the field. These findings have important implications for improving the accuracy and reliability of solutions to the problem at hand. Overall, our study contributes to the advancement of the field by providing a novel and effective method for solving the problem.

Poissonian Blurred Hyperspectral Imagery Denoising Based on Variable Splitting and Penalty Technique

Poisson noise is one of the significant sources of noise present in hyperspectral imagery (HSI). In most of the existing denoising methods, Poisson noise is first transformed into Gaussian noise through the Anscombe transform and then removed. However, the use of Anscombe transform can give rise to transform errors that affect the final denoising results. In addition, blurs often contaminate the HSI during the imaging procedure, which makes it more difficult to remove the Poisson noise. In view of the above problems, under the maximum a posteriori (MAP) model, we propose a Poissonian blurred HSI denoising based on variable splitting and penalty technique (named as VSPT) to directly remove the Poissonian blurred HSI noise without using the Anscombe transform. By finding the minimum value of the negative logarithmic Poisson log-likelihood combined with the total variation (TV), the proposed method transforms the problem into two sub-problems, which are easier to solve 1) a TV regularized deconvolution problem and 2) an ordinary convex optimization problem. The experimental results show that the proposed VSPT method can effectively remove Poisson noise in HSI contaminated by blurs during the imaging procedure.

IRS-Enabled Backscattering in a Downlink Non-Orthogonal Multiple Access System

Intelligent reflecting surface (IRS)-enabled backscatter communications can be enabled by an access point (AP) that splits its transmit signal into modulated and unmodulated parts. This letter integrates non-orthogonal multiple access (NOMA) with this method to create a two-user primary system and a secondary system of IRS data. Considering the decoding order, we maximize the rate of the strongest primary user by jointly optimizing the IRS phase shifts, power splitting (PS) factor at the AP, and NOMA power coefficients while guaranteeing the quality of service (QoS) for both weak user and IRS data in the primary and secondary systems, respectively. The resulting optimization problem is non-convex. Thus, we split it into three parts and develop an alternating optimization (AO) algorithm. The advantage is that we derive closed-form solutions for the PS factor and NOMA power coefficients in the first two parts. In the third part, we optimize the phase shifts by exploiting semi-definite relaxation (SDR) and penalty techniques to handle the unit-modulus constraints. This algorithm achieves substantial gains (e.g., 40–68%) compared to relevant baseline schemes.

Mean wind flow reconstruction of a high-rise building based on variational data assimilation using sparse pressure measurements

The paper investigates the applicability of the variational data assimilation approach to reconstruct three-dimensional wind flows around a high-rise building model, and provides guidelines towards an efficient reconstruction. The objective is to determine the best distributed control parameters based on the Reynolds-averaged-Navier–Stokes (RANS) model coupled with pressure data. The strategy considers a distributed additive forcing control parameter, acting on the momentum equation and/or the transport equation of turbulent dissipations, where the closure is performed. To avoid unphysical solutions and accelerate the optimization convergence a Sobolev gradient descent regularization is proposed and compared with penalty techniques. The proposed data assimilation framework is applied to a realistic wind engineering estimation problem combining sparse wall pressure measurements with a routinely used industrial three-dimensional RANS numerical code. Results demonstrate that wall-pressure data is a meaningful enough piece of information to recover accurately the wake flow extension. A hybrid control parameter on the transport of the dissipation and the momentum equations leads to very precise results, whereas the Sobolev gradient descent direction gives efficient regularization and a fast convergence. These findings can be useful for future application of such a data assimilation technique to wind engineering problems.

Simulating air blast on concrete structures using the volumetric penalty coupling of isogeometric analysis and peridynamics

A stabilized Isogeometric formulation of compressible flows is coupled to a large-deformation inelastic solid with an M7 Microplane constitutive model of concrete failure discretized in the framework of correspondence-based Peridynamics with bond-associated stabilization. The fluid–structure interaction (FSI) coupling makes use of a simple volumetric penalty technique that enables effective handling of the solid fracture and fragmentation. The capabilities of the FSI framework presented are demonstrated, in 3D, for point-charge detonation on concrete slabs. Slabs of varying thicknesses are simulated to capture the typical behavior of concrete under blast loading scenarios.

CONVERGENCE OF THE SIMPLE EXACT BARRIER-PENALTY FUNCTION FOR NONLIEAR MULTIOBJECTIVE OPTIMIZATION

In this paper, an extension of the new barrier penalty technical is proposed. Initially, design for nonlinear single-objective optimization with inequality constraints, we have transformed it for solving nonlinear multiobjective optimization problems with inequality constraints. First, we have provided the theoretical foundations for this extension. Secondly, we have stated convergence results of our new method to obtain Pareto optimal solutions. This work shows that the new penalty technique converges well for the determination of Pareto optimal solutions of a multiobjective optimization problems with inequality constraints.

Double phase obstacle problems with variable exponent

This paper is devoted to the study of a quasilinear elliptic inclusion problem driven by a double phase differential operator with variable exponents, an obstacle effect and a multivalued reaction term with gradient dependence. By using an existence result for mixed variational inequalities with multivalued pseudomonotone operators and the theory of nonsmooth analysis, we examine the nonemptiness, boundedness and closedness of the solution set to the problem under consideration. In the second part of the paper, we present some convergence analysis for approximated problems. To be more precise, when the obstacle function is approximated by a suitable sequence, applying a generalized penalty technique, we introduce a family of perturbed problems without constraints associated to our problem and prove that the solution set of the original problem can be approached by the solution sets of the perturbed problems in the sense of Kuratowski.

A Discontinuous Galerkin Method for the Stationary Boussinesq System

Abstract In this work we present and analyze a finite element scheme yielding discontinuous Galerkin approximations to the solutions of the stationary Boussinesq system for the simulation of non-isothermal flow phenomena. The model consists of a Navier–Stokes-type system, describing the velocity and the pressure of the fluid, coupled to an advection-diffusion equation for the temperature. The proposed numerical scheme is based on the standard interior penalty technique and an upwind approach for the nonlinear convective terms and employs the divergence-conforming Brezzi–Douglas–Marini (BDM) elements of order k for the velocity, discontinuous elements of order k - 1 {k-1} for the pressure and discontinuous elements of order k for the temperature. Existence and uniqueness results are shown and stated rigorously for both the continuous problem and the discrete scheme, and optimal a priori error estimates are also derived. Numerical examples back up the theoretical expected convergence rates as well as the performance of the proposed technique.

Optimization of System Reliability in the Imprecise Environment via Genetic Algorithm

This paper presents a genetic algorithm (GA) approach to solve the redundancy allocation problem (RAP) with imprecise parameters. The impreciseness has been considered here to tackle the unpredictable environment in real-life affairs which is directly striking the design parameters. Imprecise parameters are represented by several types of representations, viz. fuzzy, stochastic, and deterministic interval-valued. In the case of fuzzy and stochastic representations, the corresponding problems have been transformed into a deterministic interval optimization problem. Hence, to solve the problem, a GA based penalty function technique is proposed. The constraint(s) of the same are handled by constraints satisfaction rule which has been proposed in this paper. In the proposed approach, the constrained optimization problem has been converted into an unconstrained optimization problem by use of Big-M penalty technique. To solve the RAP with imprecise parameters, GA has been implemented. Finally, numerical experiments have been done for illustration purpose.

Dynamic analysis of prestressed variable stiffness composite shell structures

The design space for high-performance lightweight composite structures has grown considerably since the advent of the variable stiffness concept. In fact, variable stiffness composites have been found to improve buckling performance and dynamic stability, and to tune the structure’s dynamic response by tailoring structural stiffness. Thus, in order to exploit this wider design space, efficient linear analysis tools have an important role in preliminary design of variable stiffness structures, enabling designers to find more effective solutions when considering prestressed dynamically excited aerospace components. Considering this, a multi-domain Ritz method for eigenfrequency, transient and dynamic instability analysis of prestressed variable stiffness laminated doubly-curved shell structures is presented. Working within the first-order shear deformation theory, Sanders–Koiter shell kinematics allow general orthogonal surfaces to be modelled without further assumptions on the shallowness or on the thinness of the structure. The efficiency of the proposed Ritz method is granted by using Legendre orthogonal polynomials as displacement trial functions, while flexibility in modelling and design is given by penalty techniques that allow stiffened variable angle tow shell structures to be modelled as an assembly of shell-like domains. The proposed approach is verified by comparison with published benchmark results and finite element solutions. Original solutions are presented for a prestressed stiffened variable angle tow shell structure, which show great accuracy with an order of magnitude fewer variables when compared to standard finite element procedures, proving the reliability and efficiency of the present method in dealing with the dynamic analysis of multi-part aerospace structures.