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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.

The purpose of this paper is to study the Hölder calmness of solutions to equilibrium problems and apply it to economics.

The authors obtain the Hölder calmness by using an effective approach. More precisely, under the key assumption of strong convexity, sufficient conditions for the Hölder continuity of solution maps to equilibrium problems are established.

A new result in stability analysis for equilibrium problems and applications in economics is archived.

The authors confirm that the paper has not been published previously, is not under consideration for publication elsewhere and is not being simultaneously submitted elsewhere.

The concept of coopetition is founded on the complementarity‐based nature of this strategy. However, coopetition research has devoted relatively little attention to complementarity issues and their impact on coopetition results. By bridging the coopetition and economics of complementarities research fields, we develop a model representing a classical optimization problem in complementarities as applied to coopetition in order to evaluate potential risks deriving at an operational level from implementing a coopetition strategy. The model we develop is a situated one and is based on empirical data from a longitudinal case study of coopetition in the mineral water and soft drinks industry. The results highlight a potential risk of coopetition strategies – namely, thresholds effects – as well as the associated risks a wrong understanding of complementarities in a coopetition setting may entail.

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.

Learning field of events is characterized by the occurrenceof random and uncertain phenomena, all of which have probabilistic distributions. The meaning of learning is exchange by interdependence between interacting agents. Such agents are both the human entities and the non‐human ones. Thus, in a learning field of probabilistic events there are complex forms of interaction between the domains of mind (human cognition) and matter (world‐system). The purpose of this paper is to formalize and study such interactions by the epistemology of unity of being and becoming of relations between given variables in analytical perspective.

The critical argumentation and search in this paper leads to the premise of the episteme of unity of knowledge. It is found singularly in the doctrine of the paired universe of the Quran. The episteme of oneness of the monotheistic law and its consequential forms establish the axiomatic basis of the criterion function representing the phenomenon of probabilistic learning field. The authors refer to this criterion as wellbeing. It conceptualizes and measures the degree of unity of being and becoming that exists between the variables of a specific problem under investigation.

The results of this study formalize the probabilistic model of learning. The simulated evaluation of the probabilistic form of the wellbeing function brings out the synonymous results between unity of knowledge and its impact on the unity of the world‐system induced by the knowledge‐flows. Such a transformation of a world‐system presents the meaning of endogenous (or systemically self‐regenerated) ethics and morality in such broader fields of choices involving embedded learning systems.

The dynamics of pervasive complementarities arising from learning by unity of knowledge, and considerations of ethics and morality remain exogenous factors in economic theory. This paper, instead, has formalized ethical endogeneity in models of decision‐making with probabilistic learning fields that remain embedded in complementarities by interaction and integration across economic, social and ethical systems.

This study aims to contribute to the exploration of inter-disciplinary approaches in higher education for sustainability. It is a reflection on a case study linking students in the arts and sustainability science, through which the inter-disciplinary and problem-solving processes for solving a concrete sustainability challenge were explored.

The case study featured a workshop with students from two educational programmes at Aalborg University, namely, Art and Technology and Environmental Management and Sustainability Science, the latter being an engineering programme and the former part of the humanities. Experience evaluation was based on participant observation, written feedback and the workshop facilitators’ post-event reflections. Data analysis was based on multi-grounded theory, dialectically combining empirical data (through open coding) with relevant emergence theories. Notions of emergence were chosen because the supposed benefit of inter-disciplinarity is the emergence of novel solutions to complex problems. The study investigates the concrete conditions of emergence in educational inter-disciplinary settings.

The workshop led to a successful experience, bringing an art-based approach together with sustainability science for arriving at solutions that neither of the two would have arrived at separately. Based on participant experiences and realisations, five “emergence concepts” are suggested as supportive learning criteria and conditions, namely, “knowledge expansion”, “complementarity”, “disciplinary self-reflection”, “change of practice” and “play”.

The findings and emergence concepts can be an inspiration for creating an effective learning environment supporting the emergence of different forms of knowledge and solution concepts for solving sustainability challenges.

This paper aims to deal with the social ontology of ethnos with regard to the problem of “neutralization” of consciousness and the method of intuition.

This paper relies on the observation that the epoch we live in has originated the ontology of ethnos as a “cracked subject” connected with the dissolution of “self”.

The results show that the ontology of ethnos by itself as the synthesis of natural, social and universal forces is undergoing the asymmetric synthesis of sensual individuation and the act of thinking. However, thinking as some “fold” of the existence correlates with the extended understanding of subjectivity as the dissolution of the historical consciousness.

This paper proposes that the new ontology of ethnos is eventually connected with the “flickering” subject, with the “flickering” of the historical thinking and with the “masks” of the historical subject itself.

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.

This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP).

The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction.

This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution.

The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.

The purpose of this paper is to examine whether there are different configurations of lean bundles leading to successful (bad) financial performance and to explore how the complementarities and substitutions between lean bundles shape these configurations.

A fuzzy-set qualitative comparative analysis (fsQCA) was performed on 19 manufacturing firms. Data on financial performance (return-on-asset and growth rate) were retrieved from the AIDA database and data on the lean bundles of just-in-time, total quality management, total preventive maintenance and human resource management were collected via surveys conducted in all the plants belonging to the sampled firms.

None of the lean bundles is able to explain alone the firm’s successful financial performance. Lean bundles always have to be complemented by other lean bundles. There are different, equifinal configurations of lean bundles leading to successful (bad) financial performance. Configurations characterized by low implementation of lean bundles are related to bad financial performance.

By finding different configurations of lean bundles associated with successful and bad financial performance, this study informs operations managers on the most effective investments concerning the implementation of lean manufacturing.

This study extends literature on complementarities in lean manufacturing literature. It also bridges together apparently contradictory research on the relationship between lean manufacturing and financial performance. Finally, the study demonstrates that lean bundles have different roles in reaching successful and bad financial performance.