Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization

This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López (J. Optim. Theory Appl. 154(2), 2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements—normals and/or subdifferentials.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

The European Resonance of Napoleon’s Defeat in Spain

The military event that sealed the defeat of Napoleon in Spain was the Battle of Vitoria on 21st June 1813, which saw the allied British, Spanish and Portuguese troops led by Wellington gain victory over Joseph Bonaparte's forces. It was the last great battle of what is known in Spain as the Guerra de la Independencia, in the United Kingdom as the Peninsular War and in France as the Guerre d'Espagne. While a sliver of Spanish territory remained under French control and the war itself went on for a few more months, it was the Battle of Vitoria that marked the end of Napoleon's rule on the Iberian Peninsula, as symbolised by the departure from Spain of Joseph Bonaparte, the monarch who had been imposed five years earlier to remove the Bourbons from the Spanish throne.

Visions of the Spanish Revolution: identities and conflicts in post-welfare societies

This is a case study that analyzes photographic documents of the social protest in Spain between 2011 and 2013. The analysis is qualitative and considers the use of space, the visual expression of the messages and the orientation toward the causes or effects of political, economic and social changes. Visual sociology allows us to appreciate, in the case of the Spanish Revolution, a dynamic of “reflexivity” unrecognizable from other research approaches. Two successive waves of social mobilization in response to two different shocks can be appreciated. The first is given by political corruption, unemployment and the threat to consumer society. The second shock is caused by the savage cuts in the Welfare State. Social mobilization is expressed differently in each phase, and the forms taken by the protests show how the class structure in post industrial society shapes the reactions to the crisis of the Welfare State.

Efemérides cervantinas, ó sea Resumen cronológieo de la vida Miguel de Cervantes Saavedra,

"Obras del mismo autor": p. [5-6]

Memoria de los baños minero-medicinales de Torres : 1865 /

Incluye cuadro estadístico.

Memoria de los Baños Minero-Medicinales de la Villa de Torres en esta provincia /

Mode of access: Internet.

[Utilidad de la higiene pública : sus progresos en el presente siglo] : discurso leído en la Universidad Central... en el acto solemne de recibir la investidura de doctor en la Facultad de Medicina /

Mode of access: Internet.

Examen historico critico filosofico de la doctrina del consentimiento paterno para la celebración del matrimonio : lecciones pronunciadas en el Ateneo de Cadiz en el curso academico de 1860 a 1861 /

Mode of access: Internet.

Examen critico del tratado celebrado con Portugal en 1668 : carácter que después de él toman las relaciones de este país con el nuestro en los tiempos que siguen a dicho tratado : discurso leído en la Universidad Central... en el acto solemne de recibir la investidura de Doctor en la Facultad de Derecho, sección de derecho administrativo /

Tesis de la Universidad Central (Madrid), Facultad de Derecho, Sección de Derecho Administrativo, leída el 17-12-1860.

Ajbar Machmuâ = (colección de tradiciones) : crónica anónima del siglo XI, dada à luz por primera vez /

Mode of access: Internet.

Catálogo de los códices arábigos adquiridos en Tetuan por el Gobierno de S.M. /

Mode of access: Internet.