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The first motivation for this note is to obtain a general version
of the following result: let E be a Banach space and f : E → R be a differentiable
function, bounded below and satisfying the Palais-Smale condition; then, f is coercive,
i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and
extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references
therein.
A general result of this type was given in [3, Theorem 5.1] for a lower...
We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in , , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space are introduced....
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function.
The present paper generalizes these results to vector variational inequalities
putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced.
Under...
In this paper, we deal with strong stationarity conditions for mathematical programs with equilibrium constraints (MPEC). The main task in deriving these conditions consists in calculating the Fréchet normal cone to the graph of the solution mapping associated with the underlying generalized equation of the MPEC. We derive an inner approximation to this cone, which is exact under an additional assumption. Even if the latter fails to hold, the inner approximation can be used to check strong stationarity...
In this paper the existence of solutions to variational-type inequalities problems for (η,θ,δ)- pseudomonotone-type set-valued mappings in nonreflexive Banach spaces introduced in [4] is considered. Presented theorem does not require a compact set-valued mapping, but requires a weaker condition 'locally bounded' for the mapping.
Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris 335 (2002) 161–166] and [Puel, SIAM J. Control Optim. 48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...
Data assimilation refers to any methodology that uses partial
observational data and the dynamics of a system for estimating the
model state or its parameters. We consider here a non classical
approach to data assimilation based in null controllability
introduced in [Puel, C. R. Math. Acad. Sci. Paris335 (2002) 161–166] and [Puel, SIAM J. Control Optim.48 (2009) 1089–1111] and we apply it to oceanography.
More precisely, we are interested in developing this methodology
to recover the unknown final...
Modificando adecuadamente el método de un trabajo olvidado [1], probamos que si una aplicación continua, de un subconjunto abierto no vacío U de un espacio vectorial topológico metrizable separable y de Baire E, en un espacio localmente convexo, es direccionalmente diferenciable por la derecha en U según un subconjunto comagro de E, entonces, es genéricamente Gâteaux diferenciable en U. Nuestro resultado implica que cualquier espacio vectorial topológico, metrizable, separable y de Baire, es débilmente...
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