The cross-country correlation between social trust and income equality is well documented, but few studies examine the direction of causality. We show theoretically that by facilitating cooperation, trust may increase efficiency and lead to more equal outcomes, while the feedback from inequality to trust is ambiguous. Using a structural equations model estimated on a large country sample, we fi...

Linear equality and inequality systems with fuzzy parameters defined by the extension principle are called possibilistic linear equality and inequality systems. The solution of these systems is defined in the sense of BellmanZadeh [1]. This paper investigate stability and continuity properties of the solution in the above-named systems.

An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was tha...

In recent years, interval constraint-based solvers have shown their ability to ef£ciently solve challenging non-linear real constraint problems. However, most of the working systems limit themselves to delivering point-wise solutions with an arbitrary accuracy. This works well for equalities, or for inequalities stated for specifying tolerances, but less well when the inequalities express a set...

β1 ψ dx− ab+ α1β1. Young’s inequality [2, 1, 4] states that for every a ∈ [α1, α2] and b ∈ [β1, β2] (2) 0 ≤ F (a, b), where the equality holds iff φ(a) = b (or, equivalently, ψ(b) = a). Among the classical inequalities Young’s inequality is probably the most intuitive. Indeed, its meaning can be easily grasped once the integrals are regarded as areas below and on the left of the graph of φ (see...

We prove an inequality between three measures of disorder on the symmetric group on n elements. This inequality has been inspired by the well-known Diaconis-Graham inequalities. We also discuss when the inequality is satisfied as equality, and how often this happens. In the case n is odd, the number of permutations that satisfy the equality is a simple function of the Lucas numbers. In addition...

The authors hereby grant you non-exclusive and non-transferable license to use, copy and modify this manual for non-commercial purposes. Acknowledgements I would like to thank Frédéric Benhamou and Frédéric Goualard for many interesting discussions on interval constraint satisfaction techniques, and Luc Jaulin who gave me interesting feedback on an early version of RealPaver.

Abstract In this paper, a class of directionally differentiable multiobjective programming problems with inequality, equality and vanishing constraints is considered. Under both the Abadie constraint qualification modified qualification, Karush–Kuhn–Tucker type necessary optimality conditions are established for such nondifferentiable vector optimization by using nonlinear version Gordan theore...