In this paper, we are interested in new versions of Farkas lemmas for systems involving convex and DC-inequalities. These versions extend well-known Farkas-type results published recently, which were used as main tools in the study of convex optimization problems. The results are used to derive several strong duality results such as: Lagrange, Fenchel-Lagrange or Toland-Fenchel-Lagrange duality...

where a, b, c, and d are real constants. These systems, derived by Bona, Saut and Toland for describing small-amplitude long waves in a water channel, are formally equivalent to the classical Boussinesq system and correct through first order with regard to a small parameter characterizing the typical amplitude-todepth ratio. Exact solutions for a large class of systems are presented. The existe...

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The existence of a local curve corotating and counter-rotating vortex pairs was proven by Hmidi Mateu in via desingularization pair point vortices. In this paper, we construct global continuation these curves. That is, consider solutions which are more than mere perturbation trivial solution. Indeed, while the analysis relies on study linear equation at solution, requires deeper understanding t...

We consider a class of generalized Nash equilibrium problems (GNEPs) where both the objective functions and the constraints are allowed to depend on the decision variables of the other players. It is well-known that this problem can be reformulated as a constrained optimization problem via the (regularized) Nikaido-Isoda-function, but this reformulation is usually nonsmooth. Here we observe tha...

The significant increase in the numbers of students with autism combined with the need for better trained teachers (National Research Council, 2001) call for research on the effectiveness of alternative methods, such as consultation, that have the potential to improve service delivery. Data from 2 randomized controlled single-blind trials indicate that an autism-specific consultation planning f...

We obtained detailed quantitative and interview data from Aetna U.S. Healthcare and six physician organizations to examine changes between 1998 and 2000 in the scope of capitation contracting and delegation of responsibility for claims payment and medical management in New York and California. The physician organizations in New York included Benchmark (Continuum), Montefiore IPA, and Lenox Hill...

This paper concerns a closedness condition called (CC), requiring a convex function and a convex constrained system. This type of condition has played an important role in the study of convex optimization problems. Our aim is to establish several characterizations of this condition and to apply them to study minimizing problems involving a DC function under a cone-convex constraint and a set co...