Complementarity Problem Research Articles

Withdrawal model for fiber motions in the tuft disentanglement

Tuft disentanglement involves the principal actions of opening and carding, which are essential processing in textile technology. In this article, tuft disentanglement is modeled as fiber withdrawal considering the fiber interactions within the tuft. Based on the reasonable tuft model, the kinematic constraints were constructed in the disentanglement considering the carding essence and fiber interactions. Combined with the dynamic equation, the state of the fibers can be solved as a linear complementarity problem due to the complementarity in the fiber interactions. The withdrawal forces verified the simulations, which capture the qualitative features of experiments. Also, the effect of the withdrawal parameters on disentanglement was studied. The simulation results showed that the withdrawal forces increased with increasing withdrawal velocities and decreasing gauge lengths. The simulation results are consistent with the experiments. The proposed computational framework can be extended for predicting the mechanical behaviors of other random fibrous materials involving fiber interactions.

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

In this paper, a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed. The algorithm employs a kernel function with a linear growth term to derive the search direction, and by introducing new technical results and selecting suitable parameters, we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods. Furthermore, numerical results illustrate the efficiency of the proposed method.

Some Properties of the Solution of the Extended Vertical Tensor Complementarity Problem

Some Properties of the Solution of the Extended Vertical Tensor Complementarity Problem

Generalized modulus-based matrix splitting algorithm with Anderson acceleration strategy for vertical linear complementarity problems

The vertical linear complementarity problem (VLCP) with an arbitrary number l of matrices is related to many practical problems, of which the state-of-the-art modulus-based matrix splitting (MMS) method is proved to be an efficient solver. Enlightened by the Anderson acceleration which is a well-established and simple technique for speeding up fixed point iteration solvers with countless applications, we propose an Anderson accelerated generalized modulus-based matrix splitting (AA+GMMS) method for solving the VLCP. We particularly analyze the AA+GMMS method for the problem with l=2 and then generalize the method to any l. More importantly, the convergence theorems and theoretical optimal parameters of the MMS, AA+GMMS methods with any l are obtained in the positive definite case. Eventually, numerical experiments are given to demonstrate the effectiveness of the AA+GMMS method which significantly accelerates the original MMS method. In particular, we explore the parameters involved in the AA+GMMS method, and they have a small extent of impact on the suggested method, reinforcing that the AA+GMMS method is highly efficient.

Generalized Multilinear Games and Vertical Tensor Complementarity Problems

Generalized Multilinear Games and Vertical Tensor Complementarity Problems

A nonsmooth modified symplectic integration scheme for frictional contact dynamics of rigid–flexible multibody systems

Constructing an efficient high-order nonsmooth time-stepping integration scheme for rigid–flexible multibody systems with frictional contacts and impacts is a challenging task. This paper presents a nonsmooth modified symplectic integration scheme that can automatically achieve second-order convergence if possible. This scheme is obtained in three main steps. Firstly, the position coordinates are used to interpolate midpoint approximated integrals, which include velocity jumps implicitly; Secondly, a two-timestep central difference scheme is formulated to approximate the measure differential inclusions; Thirdly, composing two half-condensed two-timestep schemes leads to a one-timestep scheme, which retains the structure of a second-order scheme. Furthermore, while bilateral constraints are satisfied at the position level, unilateral constraints at the velocity level are subject to constraint drifts. To alleviate this issue, a classified cone complementarity problem is formulated to restrain penetration from deteriorating and sticking contacts from fictitious slipping. After time discretization, a set of nonlinear equations with cone complementarity conditions at each timestep is solved by a two-layer iterative computational strategy, where the outer layer is Newton iteration and the inner layer is a primal–dual interior point method. Several numerical examples demonstrate the high accuracy attained by the proposed method. Nonsmooth dynamics of a rigid–flexible robot involving high-speed and high-friction impacts can be simulated faster than real-time.

Inexact sequential injective algorithm for weakly univalent vector equation and its application to regularized smoothing Newton algorithm for mixed second-order cone complementarity problems

<p style='text-indent:20px;'>It is known that the complementarity problems and the variational inequality problems are reformulated equivalently as a vector equation by using the natural residual or Fischer-Burmeister function. In this paper, we first propose an inexact sequential injective algorithm (ISIA) for a vector equation, and show the global convergence under weak univalence assumption. Roughly speaking, the ISIA generates the sequence of inexact solutions of approximate vector equations, which consist of the injectives converging to the original vector-valued function. Although the ISIA is simple and conceptual, it can be a prototype to many other algorithms such as a smoothing Newton algorithm, semismooth Newton algorithm, etc. Next, we apply the ISIA prototype to the regularized smoothing Newton algorithm (ReSNA) for mixed second-order cone complementarity problems (MSOCCPs). Exploiting the ISIA convergence scheme, we prove that the ReSNA is globally convergent under Cartesian <inline-formula><tex-math id="M1">\begin{document}$ P_0 $\end{document}</tex-math></inline-formula> assumption.</p>

A novel approach to establishing uniqueness of solutions in linear complementarity problems

Linear complementarity problems are fundamental in various mathematical fields, and it is widely recognized that these problems have a unique solution if and only if the matrix related to them is a P-matrix. However, determining whether a matrix is a P-matrix can be extremely challenging or even impossible, especially for large matrices. In this paper, we present a method for establishing the existence and uniqueness of the solution to linear complementarity problems without the need for P-matrix verification.

Multi-Stage Modeling With Recourse Decisions for Solving Stochastic Complementarity Problems With an Application in Energy

Multi-Stage Modeling With Recourse Decisions for Solving Stochastic Complementarity Problems With an Application in Energy

The simplified modulus-based matrix splitting iteration method for the nonlinear complementarity problem

<abstract><p>In this paper, the simplified modulus-based matrix splitting iteration method was extended to solve the nonlinear complementarity problem, and the convergence conditions were presented from the spectral radius and the matrix norm. Then, for the special cases of this method, we provided some concrete convergence conditions as well as the quasi-optimal parameter matrix. Moreover, some numerical examples were illustrated to show the validity of the convergence results.</p></abstract>

A two-step iteration method for solving vertical nonlinear complementarity problems

A two-step iteration method for solving vertical nonlinear complementarity problems

A penalty-based method for solving a discrete HJB complementarity problem

A penalty-based method for solving a discrete HJB complementarity problem

Global error bounds for the extended vertical LCP of $ \sum-SDD $ matrices

<p>An error bound for the solution of the $ \sum-SDD $ matrix extended vertical linear complementarity problem is given when the $ \sum-SDD $ matrix satisfies the row W-property. It is shown by the illustrative example that the new bound is better than those in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup> in some cases.</p>

Novel Pareto $ Z $-eigenvalue inclusion intervals for tensor eigenvalue complementarity problems and its applications

<p>In this paper, we establish Pareto $ Z $-eigenvalue inclusion intervals of tensor eigenvalue complementarity problems based on the spectral radius of symmetric matrices deduced from the provided tensor. Numerical examples are suggested to demonstrate the effectiveness of the results. As an application we offer adequate criteria for the strict copositivity of symmetric tensors.</p>

Infinity norm bounds for the inverse of $ SDD_1^{+} $ matrices with applications

A new subclass of nonsingular $ H $-matrix named $ SDD_1^{+} $ matrices is studied in this paper. The relationships between $ SDD_1^{+} $ matrices and other subclasses of nonsingular $ H $-matrices are analyzed by numerical examples. Moreover, the infinity norm bounds of the inverse for $ SDD_1^{+} $ matrices are derived in two different methods. As applications, two error bounds of the linear complementarity problems ($ LCP $) for $ SDD_1^{+} $ matrices are given. Finally, the effectiveness of corresponding results is illustrated by numerical examples.

Complexity analysis of a predictor-corrector interior-point algorithm for $ P_{*}(\kappa) $-weighted linear complementarity problems

Complexity analysis of a predictor-corrector interior-point algorithm for $ P_{*}(\kappa) $-weighted linear complementarity problems

The Effect of Leader Perfectionism on Employee Deviance: An Interpersonal Relationship Perspective.

Despite growing evidence of significant role of leader perfectionism in the workplace, few theoretical accounts have delved into intricate dynamics of interpersonal relationships impacted by leader perfectionism, nor have they explored the extent to which these interactions might stimulate employee unethical behavior. From an interpersonal relationship perspective, based on interpersonal complementarity theory, this study proposes a link between leader perfectionism and employee deviant behavior while assessing the mediating impact of supervisor-subordinate relationship conflict, and the moderating influence of employee narcissism. This study employed three-wave surveys, with 335 employees (female 55.8%, 26-35 years old 67.4%, bachelor's degree 61.5%, worked 3-10 years 67.4%, worked with their current leader 1-5 years 66.3%) across 11 enterprises in Chinato reduce the risk of common method bias. On this basis, MPLUS 7.4 was used to test the confirmatory factor analysis of data, and SPSS 24.0 was used to test the hypotheses. (1) Leader perfectionism has a positive effect on supervisor-subordinate relationship conflict. (2) Leader perfectionism has a significantly positive effect on employee deviant behavior via supervisor-subordinate relationship conflict. (3) Employee narcissism positively moderates the relationship between leader perfectionism and supervisor-subordinate relationship conflict, and further positively moderates the indirect effect of leader perfectionism on employee deviant behavior via supervisor-subordinate relationship conflict. This study reveals the mechanism of how employee through deviant behavior as a opposition to leader perfectionism from an interpersonal relationship perspective, which provides theoretical and practical implications for reducing the negative impact of leader perfectionism and employee deviant behavior.

A relaxed two-step modulus-based matrix synchronous multisplitting iteration method for linear complementarity problems

A relaxed two-step modulus-based matrix synchronous multisplitting iteration method for linear complementarity problems

Power Dissipation and Wear Modeling in Wheel–Rail Contact

This paper is concerned with the modeling of power dissipation due to friction and its relation with wear estimation in wheel–rail contact. Wear is a complex multi-scale and multi-physical phenomenon appearing in rolling contact. Wear is generated by high contact stress and the work of friction forces. This phenomenon leads to the appearing of the worn material in the form of wear debris between contacting surfaces. In contact models, wear is usually described in terms of the wear depth function. This function modifies the gap between the contacting bodies as well as the shape of the surfaces of the wheel and rail in contact. In this paper, besides the wear depth function, the dissipated energy, rather than the contact stress, is taken into account to evaluate the wear impact on rail or wheel surfaces. The dissipated energy allows us to more precisely evaluate the wear debris amount as well as the depth of wear and its distribution along the contact interface. A two-dimensional rolling contact problem with frictional heat flow is considered. The elasto-plastic deformation of the rail is considered. This contact problem is governed by a coupled system of mechanical and thermal equations in terms of generalized stresses, displacement and temperature. The finite element method is used to discretize this problem. A discretized system of equations with nonpenetration and friction conditions is transformed and formulated as a nonlinear complementarity problem. The generalized Newton method is applied to numerically solve this mechanical subproblem. The Cholesky method is used to find the solution of the heat-conductive problem. The dissipated power is evaluated based on the resultant force and slip at a reference point. Numerical results including the distribution of slip velocity, power factor and wear rate are provided and discussed.

Approximate Message Passing for sparse matrices with application to the equilibria of large ecological Lotka–Volterra systems

This paper is divided into two parts. The first part is devoted to the study of a class of Approximate Message Passing (AMP) algorithms which are widely used in the fields of statistical physics, machine learning, or communication theory. The AMP algorithms studied in this part are those where the measurement matrix has independent elements, up to the symmetry constraint when this matrix is symmetric, with a variance profile that can be sparse. The AMP problem is solved by adapting the approach of Bayati, Lelarge, and Montanari (2015) to this matrix model.The Lotka–Volterra (LV) model is the standard model for studying the dynamical behavior of large dimensional ecological food chains. The second part of this paper is focused on the study of the statistical distribution of the globally stable equilibrium vector of a LV system in the situation where the random symmetric interaction matrix among the living species is sparse, and in the regime of large dimensions. This equilibrium vector is the solution of a Linear Complementarity Problem, which distribution is shown to be characterized through the AMP approach developed in the first part. In the large dimensional regime, this distribution is close to a mixture of a large number of truncated Gaussians.