This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which—being certainly of independent interest...

The present work was primarily motivated by our findings in the literature of some flaws within proof second-order Legendre necessary optimality condition for fractional calculus variations problems. Therefore, we were eager to elaborate a correct and it turns out that this goal is highly nontrivial, especially when considering final constraints. This paper result reflections on subject. Precis...

We propose a new class of models for image restoration and decomposition by functional minimization. Following ideas of Y. Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, our model decomposes a given (degraded or textured) image u0 into a sum u+ v. Here u ∈ BV is a function of bounded variation (a cartoon component), while the noisy (or textured) componen...

In 1957 Ky Fan gave in [5] a necessary and sufficient condition, known as Fan’s Consistency Condition, for a finite system of convex inequalities to have a solution. This result has been somewhat overshadowed by the famous Fan’s Inequality which is equivalent to Brouwer’s Fixed Point Theorem. Another result which bears Fan’s name, but which is not due to him, is Fan’s Lopsided Inequality which ...

Introduction: Much is written about the promise of Telehealth (TH) and there is great enthusiasm about its potential. However, many studies of TH do not meet orthodox quality standards. Evidence-based on assimilating findings from a few small trials of variable methodological quality presents equivocal findings and makes results difficult to interpret. Robust evidence to inform policy decisions...

This paper develops some mathematical models arising in psychology and some other areas of behavioral sciences that are formalized via general preferences with variable ordering structures. Our considerations are based on the recent “variational rationality approach” that unifies numerous theories in different branches of behavioral sciences by using, in particular, worthwhile change and stay d...

Workers and firms in a bilateral matching market choose wages and human capital investments then match assortatively. This paper studies Bayesian equilibria of finite matching games and shows that as the matching market becomes large, Bayesian equilibria can be approximated by a truncated hedonic equilibrium in the continuous matching market. We use the truncated hedonic equilibrium concept to ...

Any non-empty open convex subset of Rn is the convex hull of a complete submanifold M , of any codimension, but there are obstructions if the geometry of M is, a priori, suitably controlled at infinity. In this paper we develop tools to explore the geometry of ∂[Conv(M)] when the Grassmanian-valued Gauss map of M is uniformly continuous, a condition that, in the C2 case, is weaker than bounding...

This paper describes several dance improvisation techniques inspired by the study of the motor system. One technique takes experiments on interlimb coordination from the laboratory to the dance studio. Another technique, termed fixed-point technique, makes use of the fact that one can change which part of the body is fixed in space. A third technique is based on the idea that one can maintain t...