An improved interior-type feasible QP-free algorithm for inequality constrained optimization problems

In this paper, an improved interior-type feasible QP-free algorithm for inequality constrained optimization problems is proposed. At each iteration, by solving three systems of linear equations with the same coefficient matrix, a search direction is generated. The algorithm is proved to be globally and superlinearly convergent under some mild conditions. Preliminary numerical results show that the proposed algorithm may be promising. Advantages of the algorithm include: the uniformly nonsingularity of the coefficient matrices without the strictly complementarity condition is obtained. Moreover, the global convergence is achieved even if the number of the stationary points is infinite.     

Nonlinear explicit analysis and study of the behaviour of a new ring-type brake energy dissipator by FEM and experimental comparison

The aim of this paper is to comprehensively analyse the performance of a new ring-type brake energy dissipator through the finite element method (FEM) (formulation and finite element approximation of contact in nonlinear mechanics) and experimental comparison. This new structural device is used as a system component in rockfall barriers and fences and it is composed of steel bearing ropes, bent pipes and aluminium compression sleeves. The bearing ropes are guided through pipes bent into double-loops and held by compression sleeves. These elements work as brake rings. In important events the brake rings contract and so dissipate residual energy out of the ring net, without damaging the ropes. The rope’s breaking load is not diminished by activation of the brake. The full understanding of this problem implies the simultaneous study of three nonlinearities: material nonlinearity (plastic behaviour) and failure criteria, large displacements (geometric nonlinearity) and friction-contact phenomena among brake ring components. The explicit dynamic analysis procedure is carried out by means of the implementation of an explicit integration rule together with the use of diagonal element mass matrices. The equations of motion for the brake ring are integrated using the explicit central difference integration rule. The presence of the contact phenomenon implies the existence of inequality constraints. The conditions for normal contact are and gλ=0, where λ is the normal traction component and g is the gap function for the contact surface pair. To include frictional conditions, let us assume that Coulomb’s law of friction holds pointwise on the different contact surfaces, μ being the dynamic coefficient of friction. Next, we define the non-dimensional variable τ by means of the expression τ=t/μλ, where μλ is the frictional resistance and t is the tangential traction component. In order to find the best brake performance, different dynamic friction coefficients corresponding to the pressures of the compression sleeves have been adopted and simulated numerically by FEM and then we have compared them with the results from full-scale experimental tests. Finally, the most important conclusions of this study are given.     

On an Iyengar-type inequality involving quadratures in n knots

In this short note, we give an Iyengar-type inequality involving quadratures in n knots, where n is an arbitrary natural number.     

Generalized Hadamard's inequality and r-convex functions in Carnot groups

In this paper, we establish a generalization of Hadamard's inequality to r-convex functions on Carnot groups.     

Some mean value theorems for integrals on time scales

In this short paper, we present time scales version of mean value theorems for integrals in the single variable case.     

Using the fundamental equation of constrained motion with inequality constraints

In this paper we investigate a computational approach to keeping a moving particle within a predefined annulus or a predefined bounded space, formed by two concentric spheres with radii L_min and L_max, respectively, assuming that said particle cannot maintain a perfectly circular trajectory. The study develops an algorithm for dealing with a system in which constraints are expressed as inequalities. The proposed approach expresses the trajectory in terms of winding/unwinding logarithmic spirals with transitions, expressed as damped vibrations, between them. These transitions are necessary to resolve incompatibility between initial conditions for winding/unwinding spirals. Equations of motion for the particle are obtained by using the Fundamental Equation of Constrained Motion. The obtained simulation results show that such an approach produces the desired pseudo-periodic type of motion, and the particle stays within the predefined region of space for a long duration, although no cycle of its trajectory is repeated.     

Specialization, inequality and the social stability of economies with collective property rights

Many, if not most, economies are observed to exhibit some form of collective ownership with some goods. These economies may fail to be socially stable, in the sense that the economy has an empty core; some groups may have an incentive to ‘recontract out’. We show that, for a class of economies with collective ownership, sufficient ‘specialization’ in the endowment holdings of these economies gives rise to a non-empty core, so achieving social stability. It is shown, moreover, that reductions in income inequality are consistent with social stability, to the extent that these reductions preserve or increase ‘specialization’ in the economy. Finally, we show that our notion of specialization is not limited to the privatized sector of the economy. Even in economies in which there is no privately held property, sufficient specialization guarantees that the economy is socially stable.     

Error bounds in mathematical programming

Originated from the practical implementation and numerical considerations of iterative methods for solving mathematical programs, the study of error bounds has grown and proliferated in many interesting areas within mathematical programming. This paper gives a comprehensive, state-of-the-art survey of the extensive theory and rich applications of error bounds for inequality and optimization systems and solution sets of equilibrium problems. This work is based on research supported by the U.S. National Science Foundation under grant CCR-9624018.     

On variational aspects of some nonconvex nonsmooth global optimization problem

The paper is devoted to study a global optimization problem for a class of nonsmooth, nonconvex and non-locally Lipschitz functionals on a vector-valued reflexive Banach space. The existence of an element which is both a global minimizer and a solution of the associated hemivariational inequality is proved under some unilateral growth restrictions imposed on nonlinearities and under the assumption that an appropriately modified version of the Hedberg truncation procedure can be applied.On leave from his original institute.