Motzkin decomposition of closed convex sets via truncation

A nonempty set F is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set C with a closed convex cone D. In that case, the sets C and D are called compact and conic components of F. This paper provides new characterizations of the Motzkin decomposable sets involving truncations of F (i.e., intersections of FF with closed halfspaces), when F contains no lines, and truncations of the intersection F̂ of F with the orthogonal complement of the lineality of F, otherwise. In particular, it is shown that a nonempty closed convex set F is Motzkin decomposable if and only if there exists a hyperplane H parallel to the lineality of F such that one of the truncations of F̂ induced by H is compact whereas the other one is a union of closed halflines emanating from H. Thus, any Motzkin decomposable set F can be expressed as F=C+D, where the compact component C is a truncation of F̂. These Motzkin decompositions are said to be of type T when F contains no lines, i.e., when C is a truncation of F. The minimality of this type of decompositions is also discussed.

On the stability of the Motzkin representation of closed convex sets

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. This paper analyzes the continuity properties of the set-valued mapping associating to each couple (C,D) formed by a compact convex set C and a closed convex cone D its Minkowski sum C + D. The continuity properties of other related mappings are also analyzed.

LSA silicon material task closed-cycle process development : interim summary report, August-December 1978 /

Includes bibliographical references (page 37).

Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

* This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged.

Lower-semicontinuity and optimization of convex functionals

The result that we treat in this article allows to the utilization of classic tools of convex analysis in the study of optimality conditions in the optimal control convex process for a Volterra-Stietjes linear integral equation in the Banach space G([a, b],X) of the regulated functions in [a, b], that is, the functions f : [a, 6] → X that have only descontinuity of first kind, in Dushnik (or interior) sense, and with an equality linear restriction. In this work we introduce a convex functional Lβf(x) of Nemytskii type, and we present conditions for its lower-semicontinuity. As consequence, Weierstrass Theorem garantees (under compacity conditions) the existence of solution to the problem min{Lβf(x)}. © 2009 Academic Publications.

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Impactos da inovação nas organizações do setor da saúde: evidência empírica do CIS

Objetivos: O objetivo deste estudo é descrever o quadro de inovação no setor da saúde em Portugal, identificar os fatores críticos de sucesso da inovação, investigando os impactos da inovação nas organizações do setor da saúde. Metodologia: Na concretização da presente dissertação, recorremos a uma abordagem quantitativa, combinando a análise documental com a estatística, ao nível da análise do tratamento dos dados recolhidos através do Inquérito Comunitário à Inovação, efetuando assim um estudo de caso exploratório, descritivo e transversal. Principais resultados: As organizações analisadas operam sobretudo em mercados locais e regionais, de onde provém, maioritariamente, o seu volume de negócios, 80% do qual é composto por produtos pré-existentes. A maioria introduziu inovações de produto, processo, organizacionais ou de marketing, revelando potencial inovador. A maioria dos produtos novos ou significativamente melhorados foram desenvolvidos internamente, privilegiando fornecedores, consultores, instituições privadas de I&D e instituições do ensino superior como parceiros de cooperação, localizados sobretudo em Portugal e outros países europeus. As razões que motivam estas organizações a inovar são a melhoria da qualidade dos produtos e da capacidade de resposta a clientes e fornecedores, a diversificação da gama de produtos e o reforço da capacidade de desenvolvimento de novos produtos. Conclusões: O setor revela dinamismo na introdução de produtos novos para o mercado e para a empresa, apostando sobretudo num processo de inovação fechada. A cooperação externa é muito orientada à I&D e há um reduzido envolvimento dos agentes de mercado nas atividades de I&D através de parcerias. Contudo, estes são considerados importantes como fonte de informação e as organizações procuram responder às suas necessidades. Diferentes tipos de organizações adotam diferentes estratégias de inovação, conforme o seu mercado e a sua situação atual, o que traduz a materialização de políticas de inovação contextual, em linha com os desenvolvimentos teóricos da atualidade.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

Estudo comparativo das propriedades mecânicas em compósitos da fibra modal e poliester

In the present work, three composites with distinct reinforcements (polyester, modal e polyester + modal), all if a unsaturated orthophthalic polyester resin as matrix were used, in order to conduct a comparative study by mechanical tests and water absorption. The fibre mats were prepared in a mat preparatory by immersion developed in the Textile Engineering Laboratory. The composites were manufactured using a closed mould process by compression using an unsaturated orthophthalic polyester resin as matrix and 1% MEK (methyl ethyl ketone peroxide) as an initiator. In each composite twelve samples with the dimensions of 150x25x3 mm were cut randomly for the mechanical analysis (tension x extension, three points bending and water absorption and Scanning Electron Micsroscopy). The mechanical tests were carried out in the Laboratório de Metais e Ensaios Mecânicos UFRN . All the analyses were carried out according to the ASTM norms. The resultant samples from the mechanical analysis were subjected for the Scanning Electron Microscopy analysis. Based on the results obtained, it was observed that the reinforced composite with two fibres (modal + polyester) presented better results in comparison to the other two composites both in the tension/extension as well on the three point bending tests. In the water absorption test, it was possible to observe an equilibrium in the water absorption by the modal and polyester composite, due to the union of the two fibres. In the SEM images, the regions of rupture in the composites as well as the adsorption between the fiber and the matrix could be observed

Inclusões Dinâmicas em Escalas Temporais: Existência de Soluções sob a Hipótese de Semicontinuidade Inferior

In this paper we consider the problem of differential inclusion in time scales whose vector field is a multifunction, that is, a function that maps points to sets. It is provided conditions of existence without requiring compactness of the vector field; it is required that the vector field is closed, convex, and lower semicontinuous. In previous work in literature, it is required that the field is either scalar or compact, convex, and has closed graph.

Robust linear semi-infinite programming duality under uncertainty

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then establish that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and sufficient for robust duality. In other words, the robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with affinely parameterized data uncertainty, we establish that robust duality is easily satisfied under a Slater type constraint qualification. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-infinite linear inequalities.

Voronoi cells via linear inequality systems

The theory and methods of linear algebra are a useful alternative to those of convex geometry in the framework of Voronoi cells and diagrams, which constitute basic tools of computational geometry. As shown by Voigt and Weis in 2010, the Voronoi cells of a given set of sites T, which provide a tesselation of the space called Voronoi diagram when T is finite, are solution sets of linear inequality systems indexed by T. This paper exploits systematically this fact in order to obtain geometrical information on Voronoi cells from sets associated with T (convex and conical hulls, tangent cones and the characteristic cones of their linear representations). The particular cases of T being a curve, a closed convex set and a discrete set are analyzed in detail. We also include conclusions on Voronoi diagrams of arbitrary sets.

From the Farkas Lemma to the Hahn–Banach Theorem

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-convex function. In parallel, associated versions of a stable Farkas lemma, considering arbitrary linear perturbations of f, are also given. These new versions of the Farkas lemma, and their corresponding stable forms, are established under the weakest constraint qualification conditions (the so-called closedness conditions), and they are actually equivalent to each other, as well as equivalent to an extended version of the so-called Hahn–Banach–Lagrange theorem, and its stable version, correspondingly. It is shown that any of them implies analytic and algebraic versions of the Hahn–Banach theorem and the Mazur–Orlicz theorem for extended sublinear functions.

The Use of the Relative Interior in Integration with Nonconvex Data

Introducing an appropriate inclusion between approximate minima associated with two nonconvex functions, we derive explicit relations between the closed convex hulls of these functions. The formula we obtain goes beyond the so-called epi-pointed property of functions which is usually concerned with such a topic.