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The purpose of this paper is to present the efficient iterative methods for solving linear complementarity problems (LCP), using a class of pre-conditioners.

By using the concept of solving the fixed-point system of equations associated to the LCP, pre-conditioning techniques and Krylov subspace methods the authors design some projected methods to solve LCP. Furthermore, within the computational framework, some models of pre-conditioners candidates are investigated and evaluated.

The proposed algorithms have a simple and graceful structure and can be applied to other complementarity problems. Asymptotic convergence of the sequence generated by the method to the unique solution of LCP is proved, along with a result regarding the convergence rate of the pre-conditioned methods. Finally, a computational comparison of the standard methods against pre-conditioned methods based on Example 1 is presented which illustrate the merits of simplicity, power and effectiveness of the proposed algorithms.

Comparison between the authors' methods and other similar methods for the studied problem shows a remarkable agreement and reveals that their models are superior in point of view rate of convergence and computing efficiency.

For solving LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting such as AOR, MAOR, GAOR, SSOR, etc. But up to now, no paper has discussed the effect of pre-conditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and the authors use a class of pre-conditioners with iterative methods and analyze the convergence of these methods for LCP.

This contribution discusses a continuum model of large discrete networks in planar domains. For this model, the Kirchhoff law, boundary conditions and capacity constraints lead in a system optimisation approach to a infinite dimensional constrained optimisation problem and to “mixed” variational inequalities. Mixed finite element methods can be formulated for these variational inequalities such that computable discretizations of the continuum problem are obtained.

The purpose of this paper is to better understand complementarities-in-performance of three forms of innovations: product innovation, process innovation and organizational innovation. Additionally, complementarities-in-use for product innovation are examined, considering an additional condition: manufacturing flexibility.

Using data from 223 unlisted Portuguese industrial firms, and a fuzzy-set qualitative comparative analysis, different combinations of different forms of innovations were examined to identify complementarities-in-performance and complementarities-in-use.

Through the configurational analysis, a path to achieve high performance was uncovered, which includes the presence of both product and organizational innovations. The study also reveals that the joint absence of two conditions (from the three that were considered in the analysis) can lead to low performance. This result indicates that the relationships among the antecedent conditions are non-linear. The configurational analysis also shows that the combination of manufacturing flexibility with either process innovation or organizational innovation can lead to high product innovation. This result confirms that manufacturing flexibility is an important condition for product innovation.

The empirical evidence reported in this paper may be influenced by the definitions that were considered. Further conceptual and empirical research is encouraged to corroborate (or refute) or consolidate the findings presented herein. Moreover, although the obtained results present a high empirical coverage, other antecedent conditions beyond the scope of this study can also play an important role; for instance, marketing could influence innovation performance. Furthermore, radical innovation was not distinguished from incremental innovation when analyzing firm performance.

This study provides some clues for policy makers who aim to enhance firm performance through innovation. Managers should focus on both organizational and technological innovations, in particular product innovation, to improve firm performance. Moreover, they should be aware of the complementarities-in-use for product innovation. Considering the importance of developing product innovation to enhance performance, firms should promote high levels of product innovation. To achieve this outcome, manufacturing flexibility should be present.

Focusing on a very complex and still under-researched topic, this study contributes to the complementarities literature in several ways. This study employs a configurational approach to better understand complementarities and to integrate technological and organizational innovations. By taking this approach, this study acknowledges the existence of non-linearity and identifies not only the strategies to achieve high performance, but also the configurations that lead to low performance.

This paper extends the linear complementarity problem formulation of [7] and [8] for normal impact of planar deformable bodies in multibody systems. In the kinematics of impact we consider the normal gaps between the impacting bodies in terms of the generalized coordinates. Then, the generalized coordinate’s vector is formulated in terms of the impact forces using the 5th order implicit Runge‐Kutta approach RADAU5. Substituting the generalized coordinates in the relation of normal gaps together with the complementarity relations of unilateral contact constraints leads to a linear complementarity problem where its solution results in the solution of the impact problem including impact forces and normal gaps. Then, alternatively another formulation on velocity level based on the 4th order explicit Runge‐Kutta is presented. In the presented approach no coefficient of restitution is used for treatment of energy loss during impact and, instead, the material damping is responsible for energy loss. A good agreement between the results of our approach with the results of FEM for soft planar deformable bodies was shown in [7]. Here, we improve the results for stiff planar deformable bodies and show that with a proper selection of eigenmodes, the results on both position and velocity level approach the precise results of FEM provided that an optimal time step of the integration is chosen. We also investigate the effect of considering material damping and some higher eigenfrequencies on the amount of energy which is dissipated during impact based on our approach.

The purpose of this paper is to evaluate and contrast the welfare effects of free trade agreements (FTAs) and customs unions (CUs) on member and non‐member countries when tariffs of both members and non‐members are endogenously determined. It also aims to provide sufficient conditions under which both types of preferential trade agreement (PTA) are likely to lower tariffs on non‐members relative to that under most favored nation (MFN).

The paper employs a three country Cournot oligopoly model of trade with segmented markets.

It is shown that under symmetry CU members enjoy higher welfare relative to that under an FTA or MFN. Furthermore, the non‐member country gains from the formation of a PTA so long as the PTA's external tariff falls below a certain threshold. However, for FTA members to necessarily gain, their external tariff needs to be greater than this threshold but smaller than twice their MFN tariffs. Outside this tariff range, welfare effects of FTAs are ambiguous in the absence of further assumptions. The paper also isolates sufficient conditions under which a PTA member is less likely to impose a positive tariff on the non‐member relative to that under MFN.

Unlike existing literature, we do no assume demand linearity to obtain our main welfare results and use this assumption only for illustrative purposes. Another contribution of the paper is to provide sufficient conditions under which a PTA member is less likely to impose a positive tariff on the non‐member relative to that under MFN.

The purpose of this paper is to investigate the gaming equilibrium among fossil‐fueled generation companies (GenCos), wind generation companies, the grid company and customers participating in an emission trading (ET) market and the day‐ahead electricity market.

The complementarity method is used in this work to obtain the Nash equilibrium. By combining the Karush‐Kuhn‐Tucker (KKT) conditions of each kind of market participants with market clearing and consistency conditions, a mixed linear complementarity problem could be established.

Simulation results show that: the enforcement of ET could increase the share of generation outputs of wind generation units, and decrease the emissions from fossil‐fueled generation units; the bilateral contracts between GenCos and customers could limit the ability of exercising market power by GenCos; and when the emissions allowances allocated by the government shrink, the price of emissions allowance will increase and as the result the dispatching order of fossil‐fueled generation units will change, and the shares of generation outputs from wind generation units and combined‐cycle gas turbines increase. However, it should be mentioned that because the cost of wind generation is still very high, the increase of the share from wind generation units in the electricity market should mainly rely on cost reduction rather than the enforcement of ET.

The original contribution and the value of this study lie in developing a model framework to explore the gaming equilibrium that thermal and wind generating plants both play in the emissions trading environment and electricity market.

The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding discontinuous terms into the displacement mode, and constructing the discontinuous meshless displacement field function. In this study the contact surface equation is aimed to derive from the improved Coulomb friction contact model.

In this paper based on the basic idea of meshless method, an improved moving least squares approximation function (expansion method based on out of unit division) is applied to the analysis of two-dimensional contact problems.

On the basis of this equation after discrete processing, it is combined with the discrete form of the virtual work equation with added contact conditions, and eventually transformed into a standard linear complementary problem. Moreover, it is solved by using the Lemke algorithm, and a corresponding example is provided in this research.

The proposed method can effectively control the mutual embedding of the contact surface, and the stress distribution that is the same as the actual situation can be obtained on the contact surface.

A finite element model for the elastohydrodynamic lubrication problem is presented. A coupling between the hydrodynamic equation and the foundation compliance equation is performed, then the resulting functional problem is given an ‘extended’ variational formulation. Some preliminary numerical results are also presented.