Iterative proximal regularization of a modified Lagrangian functional for solving a semicoercive model problem with friction

The conjugate gradient is a highly effective technique to solve the unconstrained nonlinear minimization problems and it is one of the most well-known methods. It has a lot of applications. For large-scale, unconstrained minimization problems, conjugate gradient techniques are widely applied. In this paper, we will suggest a new parameter of conjugate gradient to solve the nonlinear unconstrained minimization problems, based on parameter of Dai and Liao. We will study the property of the descent ,the property of the sufficient descent and property of the global convergence a new method. We introduce some numerical data to prove the efficacy of the our method.

Convergence and error estimates for finite element solutions of elastohydrodynamic lubrication

A reduced-dimension method for unknown Crank-Nicolson finite element solution coefficient vectors of elastic wave equation with singular source term

The fuzzy support vector machine (FSVM) assigns each sample a fuzzy membership value based on its relevance, making it less sensitive to noise or outliers in the data. Although FSVM has had some success in avoiding the negative effects of noise, it uses hinge loss, which maximizes the shortest distance between two classes and is ineffective in dealing with feature noise near the decision boundary. Furthermore, whereas FSVM concentrates on misclassification errors, it neglects to consider the critical within-class scatter minimization. We present a Fuzzy support vector machine with pinball loss (FPin-SVM), which is a fuzzy extension of a reformulation of a recently proposed support vector machine with pinball loss (Pin-SVM) with several significant improvements, to improve the performance of FSVM. First, because we used the squared L2- norm of errors variables instead of the L1 norm, our FPin-SVM is a strongly convex minimization problem; second, to speed up the training procedure, solutions of the proposed FPin-SVM, as an unconstrained minimization problem, are obtained using the functional iterative and Newton methods. Third, it is proposed to solve the minimization problem directly in primal. Unlike FSVM and Pin-SVM, our FPin-SVM does not require a toolbox for optimization. We dig deeper into the features of FPin-SVM, such as noise insensitivity and within-class scatter minimization. We conducted experiments on synthetic and real-world datasets with various sounds to validate the usefulness of the suggested approach. Compared to the SVM, FSVM, and Pin-SVM, the presented approaches demonstrate equivalent or superior generalization performance in less training time.

An efficient and accurate scheme for solving the nonlinear electromagnetic inverse scattering problem on three-dimensional sparse investigation domains is proposed. The minimization problem is constructed in such a way that the data misfit between measurements and scattered fields (which are expressed as a nonlinear function of the contrast) is constrained by the contrast's first norm. The resulting minimization problem is solved using nonlinear Landweber iterations accelerated using a steepest descent algorithm. A projection operator is applied at every iteration to enforce the sparsity constraint by thresholding the result of that iteration. Steepest descent algorithm ensures accelerated and convergent solution by utilizing larger iteration steps selected based on a necessary B-condition.

Finite-element analysis of contact problems in thermoelasticity. The semi-coercive case

In this paper, a novel unconstrained convex minimization problem formulation for the Lagrangian dual of the recently introduced twin support vector machine (TWSVM) in simpler form is proposed for constructing binary classifiers. Since the objective functions of the modified minimization problems contain non-smooth `plus' function, we solve them by Newton iterative method either by considering their generalized Hessian matrices or replacing the `plus' function by a smooth approximation function. Numerical experiments were performed on a number of interesting real-world benchmark data sets. Computational results clearly illustrates the effectiveness and the applicability of the proposed approach as comparable or better generalization performance with faster learning speed is obtained in comparison with SVM, least squares TWSVM (LS-TWSVM) and TWSVM.

We present a cost-effective method for computing quantitative upper and lower bounds on linear functional outputs of exact weak solutions to the advection-diffusion-reaction equation and demonstrate a simple adaptive strategy by which such outputs can be computed to a prescribed precision. The bounds are computed from independent local subproblems resulting from a standard finite element approximation of the problem. At the heart of the method lies a local dual problem by which we transform an infinite dimensional minimization problem into a finite dimensional feasibility problem. The bounds hold for all levels of refinement on polygonal domains with piecewise polynomial forcing, and the bound gap converges at twice the rate of the ${\cal H}^1$-norm of the error in the finite element solution. The bounds are valid for any choice of model problem parameters for which an equilibrating approximate solution can befound, but they become increasingly pessimistic as the parameters tend toward the advection-dominated or reaction-dominated limits.

The paper presents a mathematical model, results of calculations and energetic characteristic of biomass fired recirculating flue gas fluidized bed boiler. Methodology of calculation and mass and energy balances were worked out according to standards PN-EN 12953 - 15 and DIN 1942. In order to develop mass and energy balances, compositions of flue gas were used. These equations create a non-linear set of equations which should be solved with the help of iterative procedure. Numerical calculations were performed using results of measurements of biomass fired fluidized bed boiler OFz-201. In next step, obtained results of thermal calculations were used to develop energetic characteristic which, take under consideration, the influence of operating conditions on energetic efficiency of boiler. Identification of model was carried out using regression methodology.

Flow of a laminar liquid film down a vertical surface

The impact of the physical model selection and rock mass stratification on the results of numerical calculations of the state of rock mass deformation around the roadways

Analytical solution of Navier-Stokes equations are extremely difficult and rare. It is one of the unsolved Clay Millennium problems in mathematics. Many solutions that exist are examples of degenerate cases where the nonlinearity is controlled. In this paper we explore the application of Bézier functions to solve the two-dimensional laminar fluid flow over a backward step. The Bézier functions provide a mesh free alternative to domain discretization methods that are currently used to solve such problems. The Navier-Stokes equation are handled directly without transformation and the setup is direct, simple, and involves minimizing the error in the residuals of the differential equations along with the error on the boundary conditions over the domain. The solutions for the velocity and pressure are available in polynomial form. They are single continuous functions over the entire domain. The procedure employs a combination of symbolic and numeric calculation in MATLAB. Two problems are explored. The first is the flow in a 2D channel to illustrate the technique. The second is the flow over the backward step. The solutions are compared to the corresponding finite element solutions from COMSOL Multiphysics software.

In order to study the influence of friction coefficient on the stiffness of disc spring, A series of disc springs ( D = 71 mm) were selected in this paper. The tension and compression experiments of disc spring components were carried out by universal testing machine. The load-displacement characteristic curves of disc springs with different friction surfaces were obtained. The results show that in the loading process, the friction effect hinders the increase of the deformation of the disc spring, so that the actual stiffness of the disc spring is improved and the actual compensation amount is reduced, so this result is worthy of attention. In order to further study the influence of friction coefficient on the loading process of disc spring, according to the load-deformation formula of disc spring in A-L method, the tangential stress caused by friction is added, and the stiffness calculation model of corresponding disc spring is established by Workbench finite element software. The coefficients of different friction surfaces are used as variables for numerical calculation. The results show that the theoretical calculation, numerical calculation and experimental results of stiffness increase with the increase of friction coefficient under 0.55 h (the compensation displacement of A71 disc spring under the working displacement of corrugated tube ±10 mm). Among them, the numerical calculation results are close to the experimental results, and the error value is less than 1%. The numerical calculation results are corrected by using the experimental data, and the corrected model calculation results are in good agreement with the measured results.

Based on graph theory, a study of via minimization problem is presented. We show that the simplest problem of this type is NP-complete and propose a heuristic algorithm for topological via minimization.

Simulation and experimental study on liner collapse of lined composite pipe