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This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.

Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.

The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.

In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

In this paper we consider the effects of certain capital market imperfections on portfolio choice problems. We show that as a result of these imperfections, the distribution functions of rates of return may depend on portfolio allocation, thus leading to non‐convexities and consequently to patterns of specialisation rather than diversification.

This paper aims to propose a robust method for non-rigid point set registration, using the Gaussian mixture model and accommodating non-rigid transformations. The posterior probabilities of the mixture model are determined through the proposed integrated feature divergence.

The method involves an alternating two-step framework, comprising correspondence estimation and subsequent transformation updating. For correspondence estimation, integrated feature divergences including both global and local features, are coupled with deterministic annealing to address the non-convexity problem of registration. For transformation updating, the expectation-maximization iteration scheme is introduced to iteratively refine correspondence and transformation estimation until convergence.

The experiments confirm that the proposed registration approach exhibits remarkable robustness on deformation, noise, outliers and occlusion for both 2D and 3D point clouds. Furthermore, the proposed method outperforms existing analogous algorithms in terms of time complexity. Application of stabilizing and securing intermodal containers loaded on ships is performed. The results demonstrate that the proposed registration framework exhibits excellent adaptability for real-scan point clouds, and achieves comparatively superior alignments in a shorter time.

The integrated feature divergence, involving both global and local information of points, is proven to be an effective indicator for measuring the reliability of point correspondences. This inclusion prevents premature convergence, resulting in more robust registration results for our proposed method. Simultaneously, the total operating time is reduced due to a lower number of iterations.

The purpose of this paper is to investigate the use of innovative workplace practices in a sample of manufacturing establishments.

The sample comprises manufacturing establishments located in Italy and a comparable sample extracted from the British Workplace Employee Relations Survey (WERS). The paper controls for sector, size, skill quality and industrial relations.

Job rotation and technical training are positively associated with current performance in both samples. On average, British establishments are more productive: the different endowment in terms of workplace practices, skills and industrial relations accounts for 40 per cent of the gap, while the different efficacy of the endowment on performance accounts for the remainder.

In both samples the introduction of team working implies a relatively important advance along the reorganisation process, which was undertaken in the early stages of reorganisation in British establishments but much later in Italian firms. Linking the progression of the reorganisation to non‐convexities in supermodular production functions may be an interesting line of future research.

Artificial intelligence (AI) has become an input to the production of goods and services. Therefore, a general question is there that “How the labor hour/human resource will be replaced by the artificial intelligence?” To answer this question, the paper considers that both AI and the human resources (HR) are the inputs to the firm and explains the choice between the two with reference to the customer relationship management. The paper derives the individual firms and the industry demand functions of the AI and the HR when both are present in the production of the identical or closely related goods and services. Moreover, the paper also shows the strategic behavior of an individual firm with the industry in selecting the AI and the HR. It has been shown that the individual firm's choice in the industry depends on the choice of the industry leader. The paper explains the supermodular game between the firms in an industry.

Game theory, industrial organization and non-convexity theories have been used in this paper to identify the choice between the HR and the AI in the customer relationship management.

The paper explains analytically the preference and demand for AI in the industry. Individual firm's strategic behavior and decision on choosing AI and the industry equilibrium have been studied logically. Moreover, the paper gives some light on the question of employment in presence of AI. The paper proves that in the presence of AI, labor demand will not be reduced but both will be used.

This work proves for the first time using some logical derivation that AI will not crowd out labor from the market. Moreover, to run AI, labor should also be used. It has been proved that to complete a job with speed and quality, both AI and HR are to be used.

In this paper, the flow of multiphase fluids in a one-dimensional homogeneous porous media involving the gravity effects is numerically studied using the dominant wave method. The paper aims to discuss these issues.

The numerical scheme used for solving the pressure equations, obtained for the black-oil model, is a backward Euler scheme while the hyperbolic mass conservation equations, derived for both black-oil and Buckley-Leverett models, are solved using the dominant wave method. Higher-order schemes are achieved using either variable derivatives along with the minmod limiter or a MUSCL type interface construction scheme using the Fromm's limiter. The mass conservation equations are solved using the first-order forward Euler method in time. Harten's entropy correction procedure is employed to avoid non-physical expansion shocks.

It was found that the dominant wave method can accurately solve multiphase flow equations involving gravity effects. Numerical experiments also show that both minmod and Fromm's limiters can be successfully used to construct higher-order schemes while the minmod limiter gives slightly more diffuse solutions.

The flow models considered here include two- and three-phase Buckley-Leverett and the black-oil models and the capillary effects are neglected.

The proposed scheme can be efficiently used for solving problems involving non-convex flux functions especially those experienced during gravity drainage process in hydrocarbon reservoirs.

To the best of authors knowledge, this is the first time that the dominant wave method has been used to tackle multiphase flow problems involving gravity effect.

The literature on household behavior contains hardly any empirical research on the within-household distributional effects of tax-benefit policies. We simulate this effect in the framework of a collective model of labor supply when shifting from a joint to an individual taxation system in France. We show that the net-of-tax relative earning potential of the wife is a significant determinant of intrahousehold negotiation but with very low elasticity. Consequently, the labor supply responses to the reform are essentially driven by the traditional substitution and income effects as in a unitary model. For some households only, the reform alters the intrahousehold distribution in a way that tends to change normative conclusions. A sensitivity analysis shows that the distributional effects captured by the collective model would be significant only for reforms both radical and of extended scope.

This paper reviews one of the crucial issues in the recent growth literature concerning the hypothesis of cross country convergence of levels and growth rates of income per capita implied by the neo‐classical growth model, both in the Solow‐Swan and Rampsey‐Cass‐Koopmans versions. The alternative endogenous growth models, consistent with permanent income inequality, are considered. Convergence to a common income level versus divergence is discussed from a theoretical point of view. Then, empirical tests of the convergence property are presented. What emerges is that Barro type regressions and their findings about “conditional” convergence are questionable and cannot be used to give a definitive response on this issue.

The purpose of this paper is to measure the financial risk and optimal capital structure of a corporation.

Irregular disjunctive programming problems arising in firm models and risk management can be solved by the techniques presented in the paper.

Parallel processing and mathematical modeling provide a fruitful basis for solving ultra-scale non-convex general disjunctive programming (GDP) problems, where the computational challenge in direct mixed-integer non-linear programming (MINLP) formulations or single processor algorithms would be insurmountable.

The test is limited to a single firm in an experimental setting. Repeating the test on large sample of firms in future research will indicate the general validity of Monte-Carlo-based VAR estimation.

The authors show that the risk surface of the firm can be approximated by integrated use of accounting logic, corporate finance, mathematical programming, stochastic simulation and parallel processing.

Parallel processing has potential to simplify large-scale MINLP and GDP problems with non-convex, multi-modal and discontinuous parameter generating functions and to solve them faster and more reliably than conventional approaches on single processors.

To follow the modern movement of using “positive feedback” to explain companies' behaviour with special focus on historical accidents.

To contribute to the emergence of new complexity theory as applied to management and prove that historical accidents matter, combining and bringing together literature sources.

The concept of unique equilibrium has been seriously disputed – the selection process is shown, as is the path dependent process using probability theory.

A location theory as case study is outlined – great for those fond of unique equilibrium.

To show another theory, which is dynamic, non‐linear, and complex as reality; to apply it to management underlying at the same time the role of historical accidents (random process).