A oferta de cursos de Licenciatura em Computação vem sendo ampliada no Brasil. Esse curso pertencente a uma área de conhecimento recente: a Computação, agregando outras áreas como a Educação. Ele encerra dificuldades que exigem discussão acadêmica e social. Uma das dificuldades é a produção de material didático para ensino de Computação; esse material é desenvolvido pelos estudantes, mas, geralmente, sem base teórica adequada. Para contribuir com a superação dessa lacuna a pesquisa objetiva analisar a influência do estudo de Epistemologia Genética e Neurociência Cognitiva na produção didática de estudantes de Licenciatura em Computação, através da elaboração de problemas ou desafios de Linguagem de Programação, para o ensino de Computação no Ensino Fundamental. As atividades foram realizadas na disciplina Práticas Articuladoras em Computação IV do curso de Licenciatura em Computação, da Universidade de Santa Cruz do Sul – UNISC, com a participação de onze estudantes. As linguagens de programação exploradas para a produção do material didático foram FMSLogo, Scratch e Robokit. O levantamento dos dados contou com quatro etapas que compreenderam a produção didática dos estudantes através do desenvolvimento de problemas ou desafios de programação, o estudo das referidas teorias, em especial as categorias “Aprendizagem”, “Emoções e Sentimentos”, “Estímulo Emocional Competente”, “Abstração Reflexionante” e “Self”, a reelaboração da produção didática com base no estudo realizado e a análise dessa produção Os dados junto aos estudantes matriculados na disciplina foram coletados através de entrevista oral e de questionário online. A análise do material didático, desenvolvido pelos estudantes, verifica a presença textual dos três primeiros elementos de referência da prática computacional estabelecidos pelo Instituto de Tecnologia de Massachusetts – MIT: 1. Ação interativa-incremental, 2. Teste-depuração, 3.Reutilização-reformulação e 4.Abstração-modulação. A análise dos processos de abstração pseudoempírica e reflexionante permitiram entender que os resultados apontam a influência do estudo de Epistemologia Genética e Neurociência Cognitiva na produção didática dos estudantes de Licenciatura em Computação. Os problemas de programação reelaborados por nove estudantes apresentam modificações intermediárias ou muitas modificações. Conclui-se que a produção de material didático para o ensino de Computação no Ensino Fundamental pode assumir um caráter desafiador, através de descrição textual que privilegia a ação de quem resolve problemas de programação. / The offer of graduation programs in Computer Science for Teaching has been expended in Brazil. This graduation program belongs to a recent area of knowledge: Computing, adding other areas such as Education. It entails difficulties that require academic and social discussion. One of the difficulties is the production of didactic material for Computing Teaching; this material is developed by the students, but generally without adequate theoretical basis. In order to contribute to overcoming this gap, the objective research decided to analyze the influence of the study Genetic Epistemology and Cognitive Neuroscience in the didactic production of undergraduate students in Computer Science for Teaching, through the elaboration of problems or challenges of Programming Language, for the Computing Teaching in Elementary School. The Method relied on activities carried out in the subject Articulating Practices in Computing IV of the in Computer Science for Teaching course of the University of Santa Cruz do Sul – UNISC, with the participation of eleven students. The programming languages explored for the production of didactic material were FMSLogo, Scratch and ROBOKIT. The data collection had four stages that comprised the didactic production of the students through the development of problems or programming challenges, the study of these theories, in particular the categories “learning”, “emotions and feelings”, “competent emotional stimulus”, “reflective abstraction” and “self” the re-elaboration of didactic production based on the realized study and the analysis of this production The collected data from the enrolled students in the subject were collected through an interview based on the Jean Piaget Clinical Method and an online questionnaire. The analysis of the didactic material, developed by the students, verifies the textual presence of the first three elements of computational practice established by the Massachusetts Institute of Technology - MIT: 1. Interactive-incremental action, 2. Test-Depuration, 3. Reuse-reformulation and 4. Abstraction-modulation. The analysis of the processes of pseudoempirical and reflective abstraction processes allowed to understand that the results point to the influence of Genetic Epistemology and Cognitive Neuroscience study in the didactic production of Computer Science for Teaching students. Programming problems reworked by nine students present intermediate modifications or many modifications. It is concluded that the production of didactic material for the Computing teaching in the elementary school can assume a challenging character, through a textual description that privileges the action of those who solve programming problems.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-09-04T12:20:42Z No. of bitstreams: 1 erickmariodonascimentooliveira.pdf: 3492871 bytes, checksum: 845fa85f6d95efe2e7ad13563f342bc3 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-09-04T13:21:49Z (GMT) No. of bitstreams: 1 erickmariodonascimentooliveira.pdf: 3492871 bytes, checksum: 845fa85f6d95efe2e7ad13563f342bc3 (MD5) / Made available in DSpace on 2018-09-04T13:21:49Z (GMT). No. of bitstreams: 1 erickmariodonascimentooliveira.pdf: 3492871 bytes, checksum: 845fa85f6d95efe2e7ad13563f342bc3 (MD5) Previous issue date: 2018-06-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho é apresentado o comportamento do algoritmo IED quando aplicado a problemas de programação em dois níveis. Para isso, o problema do seguidor é substituído pelas condições necessárias de primeira ordem de Karush-Kuhn-Tucker e, dessa maneira, o problema de programação em dois níveis é transformado em um problema de otimização com restrições não lineares. Dessa forma, as condições necessárias para utilização do algoritmo IED (Interior Epigraph Directions) são satisfeitas. Esse método tem como característica resolver problemas de otimização não convexa e não diferenciáveis via utilização da técnica de dualidade Lagrangiana, onde as funções de restrições são introduzidas na função objetivo para formar a função Lagrangiana. Além disso, o método considera o problema dual induzido por um esquema generalizado da dualidade Lagrangiana aumentada e obtém a solução primal produzindo uma sequência de pontos no interior do epígrafo da função dual. Dessa forma, o valor da função dual, em algum ponto do espaço dual, é dado pela minimização da Lagrangiana. Por fim, experimentos numéricos são apresentados em relação à utilização do algoritmo IED em problemas de programação em dois níveis encontrados na literatura. / This work presents the behavior of the IED algorithm when applied to bilevel programming problems. For this, the follower problem is replaced by the first-order necessary Karush-Kuhn-Tucker’s conditions and thus, the problem of bilevel programming turns into an optimization problem with non-linear constraints. Thus, the conditions required for use of the IED (Interior Epigraph Directions) algorithm are satisfied. This method has the characteristic of solving non-convex and non-differentiable optimization problems using the Lagrangian duality technique, where the constraint functions are introduced into the objective function for formulation of the Lagrangian. Furthermore, the method considers the dual problem induced by a generalized scheme of augmented Lagrangian duality and obtains the primal solution by producing a sequence of points inside the dual function epigraph. Then the value of the dual function, at some point in the dual space, is given by Lagrangian minimization. Finally, numerical experiments are presented showing the use of the IED algorithm in bilevel programming problems found in the literature.

This thesis presents the mixed integer bilevel programming problems where some optimality conditions and solution algorithms are derived. Bilevel programming problems are optimization problems which are partly constrained by another optimization problem. The theoretical part of this dissertation is mainly based on the investigation of optimality conditions of mixed integer bilevel program. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. After that, we are able to discuss local optimality conditions using tools of variational analysis for each different approach. Moreover, bilevel optimization problems with semidefinite programming in the lower level are considered in order to formulate more optimality conditions for the mixed integer bilevel program. We end the thesis by developing some algorithms based on the theory presented

Při práci s úlohami stochastického programování se často setkáváme s optimalizačními problémy, které jsou příliš rozsáhlé na to, aby byly zpracovány pomocí rutinních metod matematického programování. Nicméně, v některých případech mají tyto problémy vhodnou strukturu, umožňující použití specializovaných dekompozičních metod, které lze použít při řešení rozsáhlých optimalizačních problémů. Tato práce se zabývá dvěma třídami úloh stochastického programování, které mají speciální strukturu, a to dvoustupňovými stochastickými úlohami a úlohami s pravděpodobnostním omezením, a pokročilými dekompozičními metodami, které lze použít k řešení problému v těchto dvou třídách. V práci popisujeme novou metodu pro tvorbu “warm-start” řezů pro metodu zvanou “Generalized Benders Decomposition”, která se používá při řešení dvoustupňových stochastických problémů. Pro třídu úloh s pravděpodobnostním omezením zde uvádíme originální dekompoziční metodu, kterou jsme nazvali “Pool & Discard algoritmus”. Užitečnost popsaných dekompozičních metod je ukázána na několika příkladech a inženýrských aplikacích.

As the title already suggests the aim of the present work is to present Farkas - type results for inequality systems involving convex and/or non - convex functions. To be able to give the desired results, we treat optimization problems which involve convex and composed convex functions or non - convex functions like DC functions or fractions. To be able to use the fruitful Fenchel - Lagrange duality approach, to the primal problem we attach an equivalent problem which is a convex optimization problem. After giving a dual problem to the problem we initially treat, we provide weak necessary conditions which secure strong duality, i.e., the case when the optimal objective value of the primal problem coincides with the optimal objective value of the dual problem and, moreover, the dual problem has an optimal solution. Further, two ideas are followed. Firstly, using the weak and strong duality between the primal problem and the dual problem, we are able to give necessary and sufficient optimality conditions for the optimal solutions of the primal problem. Secondly, provided that no duality gap lies between the primal problem and its Fenchel - Lagrange - type dual we are able to demonstrate some Farkas - type results and thus to underline once more the connections between the theorems of the alternative and the theory of duality. One statement of the above mentioned Farkas - type results is characterized using only epigraphs of functions. We conclude our investigations by providing necessary and sufficient optimality conditions for a multiobjective programming problem involving composed convex functions. Using the well-known linear scalarization to the primal multiobjective program a family of scalar optimization problems is attached. Further to each of these scalar problems the Fenchel - Lagrange dual problem is determined. Making use of the weak and strong duality between the scalarized problem and its dual the desired optimality conditions are proved. Moreover, the way the dual problem of the scalarized problem looks like gives us an idea about how to construct a vector dual problem to the initial one. Further weak and strong vector duality assertions are provided.

As the title already suggests the aim of the present work is to present Farkas - type results for inequality systems involving convex and/or non - convex functions. To be able to give the desired results, we treat optimization problems which involve convex and composed convex functions or non - convex functions like DC functions or fractions. To be able to use the fruitful Fenchel - Lagrange duality approach, to the primal problem we attach an equivalent problem which is a convex optimization problem. After giving a dual problem to the problem we initially treat, we provide weak necessary conditions which secure strong duality, i.e., the case when the optimal objective value of the primal problem coincides with the optimal objective value of the dual problem and, moreover, the dual problem has an optimal solution. Further, two ideas are followed. Firstly, using the weak and strong duality between the primal problem and the dual problem, we are able to give necessary and sufficient optimality conditions for the optimal solutions of the primal problem. Secondly, provided that no duality gap lies between the primal problem and its Fenchel - Lagrange - type dual we are able to demonstrate some Farkas - type results and thus to underline once more the connections between the theorems of the alternative and the theory of duality. One statement of the above mentioned Farkas - type results is characterized using only epigraphs of functions. We conclude our investigations by providing necessary and sufficient optimality conditions for a multiobjective programming problem involving composed convex functions. Using the well-known linear scalarization to the primal multiobjective program a family of scalar optimization problems is attached. Further to each of these scalar problems the Fenchel - Lagrange dual problem is determined. Making use of the weak and strong duality between the scalarized problem and its dual the desired optimality conditions are proved. Moreover, the way the dual problem of the scalarized problem looks like gives us an idea about how to construct a vector dual problem to the initial one. Further weak and strong vector duality assertions are provided.

This thesis presents the mixed integer bilevel programming problems where some optimality conditions and solution algorithms are derived. Bilevel programming problems are optimization problems which are partly constrained by another optimization problem. The theoretical part of this dissertation is mainly based on the investigation of optimality conditions of mixed integer bilevel program. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. After that, we are able to discuss local optimality conditions using tools of variational analysis for each different approach. Moreover, bilevel optimization problems with semidefinite programming in the lower level are considered in order to formulate more optimality conditions for the mixed integer bilevel program. We end the thesis by developing some algorithms based on the theory presented