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We consider nonlinear mappings f :X → Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x̄, that is, metric regularity of f from X into themetric space E = f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves...

A reduction method is proposed which allows standard sensitivity techniques for variational inequalities to applied to equilibrium network ̄ow problems without additional assumptions on either the underlying network or the numbers of active paths. In particular it is shown that under mild regularity conditions, small perturbations of equilibria can be given an explicit arc̄ow representation whic...

In a transit network involving vehicles with rigid capacities, we advocate the use of strategies for describing consumer behavior. At each boarding node, a user sorts the transit lines in decreasing order of preference, and boards the first vehicle in this list whose residual capacity is nonzero. Since a user’s position in the queue varies from day to day, the delay experienced is stochastic. T...

An objective method for homogenization of early (pre $1850) instrumental near surface air temperature records is developed. The method is grounded on the same variational principle as used in the objective analysis of meteorological ®elds; i.e. the method consists of a statistically optimal spatial-coherence-based adjustment of nearby station temperature records. The adjustments are made for se...

Abstract. We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic, momentum preserving, and can be constructed to be of arbitrarily high-order, or can be made to converge geometrically. Furthermore, these methods are stable and accurate for very large time steps. We demonstrate the construction of one such variational integrator ...

We propose an approximate method to obtain the speed of wavefronts. It is built up from a known variational principle. For a range of systems of biological and physical interest, comparison to previously-known solutions and to numerical simulations shows the powerfulness of our approximate technique. For time-delayed equations, we also propose an alternative approximate solution, based on the r...

Convexity has long had an important role in economic theory, but some recent developments have featured it all the more in problems of equilibrium. Here the tools of convex analysis are applied to a basic model of incomplete financial markets in which assets are traded and money can be lent or borrowed between the present and future. The existence of an equilibrium is established with technique...

In matricial analysis, the theorem of Eckart & Young provides a best approximation of an arbitrary matrix by a matrix of rank at most r. In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially t...

Modern variational analysis provides a sophisticated unification of convex and smooth optimization theory, achieving striking generality but at the expense of possible pathology. The general theory must handle highly irregular and oscillatory functions and sets, and yet, on the other hand, a rich family of concrete instances involve no such pathology. In particular, from a variety of variationa...