Penalty Technique Research Articles

Fast total variation deconvolution for blurred image contaminated by Poisson noise

In this paper, we present a fast non-blind deconvolution method for restoring blurred images contaminated by Poisson noise. The problem is formulated by finding the minimizer of the negative logarithmic Poisson log-likelihood combined with the total variation (TV). To attack the challenging task, we adopt the well-known variable splitting and penalty technique to convert the problem into two easier sub-problems: one is a modified TV regularized deconvolution and the other is a simple convex optimization problem. Experimental results show that the proposed method runs very fast and the quality of the restored image is comparable with that of some state of the art methods.

Construction and solution of an adaptive image-restoration model for removing blur and mixed noise

We establish a practical regularized least-squares model with adaptive regularization for dealing with blur and mixed noise in images. This model has some advantages, such as good adaptability for edge restoration and noise suppression due to the application of a priori spatial information obtained from a polluted image. We further focus on finding an important feature of image restoration using an adaptive restoration model with different regularization parameters in polluted images. A more important observation is that the gradient of an image varies regularly from one regularization parameter to another under certain conditions. Then, a modified graduated nonconvexity approach combined with a median filter version of a spatial information indicator is proposed to seek the solution of our adaptive image-restoration model by applying variable splitting and weighted penalty techniques. Numerical experiments show that the method is robust and effective for dealing with various blur and mixed noise levels in images.

Post-Buckling Analysis of Damaged Multilayered Composite Stiffened Plates by Rayleigh-Ritz Method

A Rayleigh-Ritz approach for the analysis of buckling and post-buckling behavior of cracked composite stiffened plates is presented. The structure is modeled as the assembly of plate elements modeled by the first order shear deformation theory and taking geometric nonlinearities into account through the von Karman’s theory assumptions. Continuity along the plate elements connected edges and the enforcement of rigid and elastic restraints of the plate boundaries are obtained by using penalty techniques, which also allow to straightforwardly implement efficient crack modeling strategies. General symmetric and unsymmetric stacking sequences are considered and numerical procedures have been developed and used to validate the present solution by comparison with FEA results. Original results are presented for post-buckling solution of multilayered stiffened plates with through-the-thickness cracks, showing the effects of large displacements on the cracked plate post-buckling behavior.

A reduction method for nonlinear semi-infinite programming based on an exact penalty technique

Semi-infinite programming (SIP) problems arise in several areas of engineering, such as robot trajectory planning, production planning, design of digital filters and air pollution control. Despite its large applicability there is not much software available to solve such problems. The only available SIP solvers are the fseminf MATLAB function, FSQP and NSIPS, but none of these solvers provide an algorithm belonging to the class of reduction type methods. In this article we propose a reduction type method, based on a penalty technique to solve SIP problems. We report numerical results with 117 test problems from the SIPAMPL database, using a MATLAB implementation of the proposed algorithm, which we coined as SiRedAl.

A New Algorithm Framework for Image Inpainting in Transform Domain

In this paper, we focus on variational approaches for image inpainting in transform domain and propose two new algorithms, iterative coupled transform domain inpainting (ICTDI) and iterative decoupled transform domain inpainting. In the derivation of ICTDI, we use operator splitting and the quadratic penalty technique to get a new approximate problem of the basic model. By the alternating minimization method, the approximate problem can be decomposed as three relatively simple subproblems with closed-form solutions. However, ICTDI is not efficient when some adaptive regularization operator is used, such as the learned BM3D frame. To overcome this drawback, with some modifications, we decouple our framework into three relatively independent parts: denoising, linear combination in the transform domain, and linear combination in the image domain. Therefore, we can use any existing denoising method in the denoising step. We consider three choices for regularization operators in our approach: gradient operator...

A unifying theory of exactness of linear penalty functions

In this article, we develop a theory of exact linear penalty functions that generalizes and unifies most of the results on exact penalization existing in the literature. We discuss several approaches to the study of both locally and globally exact linear penalty functions, and obtain various necessary and sufficient conditions for the exactness of a linear penalty function. We pay more attention than usual to necessary conditions, which allows us to deeply understand the exact penalty technique.

Machine learning derived risk prediction of anorexia nervosa.

BackgroundAnorexia nervosa (AN) is a complex psychiatric disease with a moderate to strong genetic contribution. In addition to conventional genome wide association (GWA) studies, researchers have been using machine learning methods in conjunction with genomic data to predict risk of diseases in which genetics play an important role.MethodsIn this study, we collected whole genome genotyping data on 3940 AN cases and 9266 controls from the Genetic Consortium for Anorexia Nervosa (GCAN), the Wellcome Trust Case Control Consortium 3 (WTCCC3), Price Foundation Collaborative Group and the Children’s Hospital of Philadelphia (CHOP), and applied machine learning methods for predicting AN disease risk. The prediction performance is measured by area under the receiver operating characteristic curve (AUC), indicating how well the model distinguishes cases from unaffected control subjects.ResultsLogistic regression model with the lasso penalty technique generated an AUC of 0.693, while Support Vector Machines and Gradient Boosted Trees reached AUC’s of 0.691 and 0.623, respectively. Using different sample sizes, our results suggest that larger datasets are required to optimize the machine learning models and achieve higher AUC values.ConclusionsTo our knowledge, this is the first attempt to assess AN risk based on genome wide genotype level data. Future integration of genomic, environmental and family-based information is likely to improve the AN risk evaluation process, eventually benefitting AN patients and families in the clinical setting.Electronic supplementary materialThe online version of this article (doi:10.1186/s12920-016-0165-x) contains supplementary material, which is available to authorized users.

High-fidelity numerical simulation of solitons in the nerve axon

High-order accurate finite difference schemes are derived for a non-linear soliton model of nerve signal propagation in axons. Two types of well-posed boundary conditions are analysed. The boundary closures are based on the summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP-SAT approximation is time-integrated with an explicit finite difference method. The accuracy and stability properties of the newly derived finite difference approximations are demonstrated for an analytic soliton solution.

A combined finite element and oversampling multiscale Petrov–Galerkin method for the multiscale elliptic problems with singularities

In this paper, we construct a combined finite element and oversampling multiscale Petrov-Galerkin method (FE-OMsPGM) to solve the multiscale problems which may have singularities in some special portions of the computational domain. For example, in the simulation of subsurface flow, singularities lie in the porous media with channelized features, or in near-well regions since the solution behaves like the Green function. The basic idea of FE-OMsPGM is to utilize the traditional finite element method (FEM) directly on a fine mesh of the problematic part of the domain and using the Petrov-Galerkin version of oversampling multiscale finite element method (OMsPGM) on a coarse mesh of the other part. The transmission condition across the FE-OMsPG interface is treated by the penalty technique. The FE-OMsPGM takes advantages of the FEM and OMsPGM, which uses much less DOFs than the standard FEM and may be more accurate than the OMsPGM for problems with singularities. Although the error analysis is carried out under the assumption that the oscillating coefficients are periodic, our method is not restrict to the periodic case. Numerical examples with periodic and random highly oscillating coefficients, as well as the multiscale problems on the L-shaped domain, and multiscale problems with high contrast channels or well-singularities are presented to demonstrate the efficiency and accuracy of the proposed method.

DC programming approaches for discrete portfolio optimization under concave transaction costs

The paper investigates DC programming and DCA for both modeling discrete portfolio optimization under concave transaction costs as DC programs, and their solution. DC reformulations are established by using penalty techniques in DC programming. A suitable global optimization branch and bound technique is also developed where a DC relaxation technique is used for lower bounding. Numerical simulations are reported that show the efficiency of DCA and the globality of its computed solutions, compared to standard algorithms for nonconvex nonlinear integer programs.

Pengaruh Jumlah Alternatif Jawaban dan Teknik Penskoran terhadap Reliabilitas Tes

<p>This study aimed to determine the effect of the number of alternative answers <br />and scoring techniques to reliability test. Forms of this test includes multiple choice test three answer choice and multiple choice test four answer choices with penalty scoring techniques (Punishment Score) and scoring techniques compensation (Reward Score). The method uses the experiment, while the designused istreatment bylevel 2 x 2. Research hypotheses were tested using two way analysis of variance (ANOVA). The result concluded that: (1) reliability tests with three multiple choice answer options is higher than the multiple choice test four answer choices, (2) reliability tests with scoring techniques penalty higher than the reliability of the technique of scoring compensation, <br />and (3) No interaction between the number of alternative answers to the scoring <br />technique. The results of this study can be considered for the teacher to give test using a form of multiple choice test three answer choice and multiple choice test four answer choices test scoring with a penalty techniques. <br /> <br />Keywords : reliability, scoring techniques, alternative answers.</p>

Fair Scheduling for Energy Harvesting Nodes

This letter considers the problem of scheduling in the multiple input multiple output (MIMO) multiple-access wireless channel, where the transmitters are energy harvesting nodes (EHNs) that are powered by renewable energy sources (RESs). In this letter the conventional scheduling objective of maximizing rate is augmented by two other objectives, regulating fairness, and stabilization of the stored energy processes of the EHNs. This problem is formulated as a network of energy queues, which represent the batteries. Considering the stochastic nature of the wireless channel and the energy harvesting processes, this letter employs Lyapunov drift plus penalty technique to develop a cross-layer scheduler that operates in a slotted-time and distributed manner. At each epoch it selects an EHN for transmission and computes the transmit power. As an added advantage, the power control algorithm still retains the optimal water-filling solution. Through simulations, the proposed solution is compared against a conventional max-rate scheduler and is shown to better enforce fairness, stabilize the battery levels, and minimize the required battery capacity.

Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state

An adaptive finite element method is developed for a class of optimal control problems with elliptic variational inequality constraints and objective functionals defined on the space of continuous functions, necessitated by a point-tracking requirement with respect to the state variable. A suitable first order stationarity concept is derived for the problem class via a penalty technique. The dual-weighted residual approach for goal-oriented adaptive finite elements is applied and relies on the stationarity system. It yields primal residuals weighted by approximate dual quantities and vice versa as well as complementarity mismatch errors. A report on numerical tests, including the critical case of biactivity, completes this work.

Post-buckling analysis of cracked multilayered composite plates by pb-2 Rayleigh–Ritz method

A pb-2 Rayleigh–Ritz variational approach for the analysis of post-buckling behavior of cracked composite plates is presented. The plate is modeled by the first order shear deformation theory taking geometric nonlinearities into account through the von Karman’s theory. General stacking sequences are considered. Cracks are modeled by using subdomain decomposition of the plate coupled with penalty techniques, used to augment the variational statement with the needed continuity conditions along the connected subdomains edges. Numerical procedures have been developed and used to validate the present solution by comparison with available literature results. Original results are then presented for post-buckling solution of representative symmetric and unsymmetric multilayered plates with through-the-thickness cracks, showing the effects of large displacements on the cracked plate post-buckling behavior.

Entropy stable wall boundary conditions for the three-dimensional compressible Navier–Stokes equations

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier–Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Image deblurring associated with shearlet sparsity and weighted anisotropic total variation

Image deblurring is one of the classical problems in image processing. The main purpose of image deblurring is to restore the images corrupted by blur and additive noise while preserving edges and details. We focus on the nonblind image deblurring (NBID) problem. In order to obtain good deblurred images, we propose an NBID method based on a compound regularization model associated with the shearlet-based sparsity and the weighted anisotropic total variation. Based on this model, we present an alternative iterative scheme which consists of the operator splitting and penalty techniques. The split Bregman-based multivariable minimization iteration is introduced to optimize the proposed NBID inverse problem. Compared with some previous methods, the experiments demonstrate the efficiency and viability of the proposed method for preserving sharp edges and structural details of the image while mitigating the artifacts.

High-fidelity numerical simulation of the dynamic beam equation

A high-fidelity finite difference approximation of the dynamic beam equation is derived. Different types of well-posed boundary conditions are analysed. The boundary closures are based on the summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP–SAT approximation leads to fully explicit time integration. The accuracy and stability properties of the newly derived SBP–SAT approximations are demonstrated for both 1-D and 2-D problems.

Sparse semi-supervised support vector machines by DC programming and DCA

This paper studies the problem of feature selection in the context of Semi-Supervised Support Vector Machine (S3VM). The zero norm, a natural concept dealing with sparsity, is used for feature selection purpose. Due to two nonconvex terms (the loss function of unlabeled data and the ℓ0 term), we are faced with a NP hard optimization problem. Two continuous approaches based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) are developed. The first is DC approximation approach that approximates the ℓ0-norm by a DC function. The second is an exact reformulation approach based on exact penalty techniques in DC programming. All the resulting optimization problems are DC programs for which DCA are investigated. Several usual sparse inducing functions are considered, and six versions of DCA are developed. Empirical numerical experiments on several Benchmark datasets show the efficiency of the proposed algorithms, in both feature selection and classification.

DC approximation approaches for sparse optimization

Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC (Difference of Convex functions) programming framework. Considering a common DC approximation of the zero-norm including all standard sparse inducing penalty functions, we studied the consistency between global minimums (resp. local minimums) of approximate and original problems. We showed that, in several cases, some global minimizers (resp. local minimizers) of the approximate problem are also those of the original problem. Using exact penalty techniques in DC programming, we proved stronger results for some particular approximations, namely, the approximate problem, with suitable parameters, is equivalent to the original problem. The efficiency of several sparse inducing penalty functions have been fully analyzed. Four DCA (DC Algorithm) schemes were developed that cover all standard algorithms in nonconvex sparse approximation approaches as special versions. They can be viewed as, an l1-perturbed algorithm/reweighted-l1 algorithm / reweighted-l2 algorithm. We offer a unifying nonconvex approximation approach, with solid theoretical tools as well as efficient algorithms based on DC programming and DCA, to tackle the zero-norm and sparse optimization. As an application, we implemented our methods for the feature selection in SVM (Support Vector Machine) problem and performed empirical comparative numerical experiments on the proposed algorithms with various approximation functions.

An Unconditionally Energy Stable Penalty Immersed Boundary Method for Simulating the Dynamics of an Inextensible Interface Interacting with a Solid Particle

In this paper, a novel penalty method based on the immersed boundary formulation is proposed for simulating the transient Stokes flow with an inextensible interface enclosing a suspended solid particle. The main idea of this approach relies on the penalty techniques by modifying the constitutive equation of Stokes flow to weaken the incompressibility condition, relating the surface divergence to the elastic tension $$\sigma $$? to relax the interface's inextensibility, and connecting the particle surface-velocity with the particle surface force $${\varvec{F}}$$F to regularize the particle's rigid motion. The advantage of these regularized governing equations is that when they are discretized by the standard centered difference scheme on a staggered grid, the resulting linear system can easily be reduced by eliminating the unknowns $$p_h, \sigma _h$$ph,?h and $${\varvec{F}}_h$$Fh directly, so that we just need to solve a smaller linear system of the velocity approximation $${\varvec{u}}_h$$uh. This advantage is preserved and even enhanced when such approach is applied to the transient Stokes flow with multiple compound vesicles. Moreover, this smaller linear system is symmetric and negative-definite, which enables us to use efficient linear solvers. Another important feature of the proposed method is that the discretization scheme is unconditionally stable in the sense that an appropriately defined energy functional associated with the discrete system is decreasing and hence bounded in time. We numerically test the accuracy and stability of the immersed boundary discretization scheme. The tank-treading and tumbling motions of inextensible interface with a suspended solid particle in the simple shear flow will be studied extensively. The simulation of the motion of multiple compound vesicles will be performed as well. Numerical results illustrate the superior performance of the proposed penalty method.