Mirror-Descent Methods in Mixed-Integer Convex Optimization

In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an algorithmic approach to this problem, postponing its hardness to the realization of an oracle. If this oracle can be realized in polynomial time, then the problem can be solved in polynomial time as well. For problems with two integer variables, we show that the oracle can be implemented efficiently, that is, in O(ln(B)) approximate minimizations of f over the continuous variables, where B is a known bound on the absolute value of the integer variables.Our algorithm can be adapted to find the second best point of a purely integer convex optimization problem in two dimensions, and more generally its k-th best point. This observation allows us to formulate a finite-time algorithm for mixed-integer convex optimization

Exact Solution Methods for the kk-item Quadratic Knapsack Problem

The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method. We review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.Comment: 12 page

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

On generalized surrogate duality in mixed-integer nonlinear programming

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global -optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solvers can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments

Educomunicação e suas áreas de intervenção: Novos paradigmas para o diálogo intercultural

oai:omp.abpeducom.org.br:publicationFormat/1O material aqui divulgado representa, em essência, a contribuição do VII Encontro Brasileiro de Educomunicação ao V Global MIL Week, da UNESCO, ocorrido na ECA/USP, entre 3 e 5 de novembro de 2016. Estamos diante de um conjunto de 104 papers executivos, com uma média de entre 7 e 10 páginas, cada um. Com este rico e abundante material, chegamos ao sétimo e-book publicado pela ABPEducom, em seus seis primeiros anos de existência. A especificidade desta obra é a de trazer as “Áreas de Intervenção” do campo da Educomunicação, colocando-as a serviço de uma meta essencial ao agir educomunicativo: o diálogo intercultural, trabalhado na linha do tema geral do evento internacional: Media and Information Literacy: New Paradigms for Intercultural Dialogue

Differentiation of BP-type baculovirus strains using in situ hybridization

BP-type viruses infect wild and farmed shrimp species in the Americas and can cause high mortality in larval stages. Histologically, BP disease is characterized by the presence of occlusion bodies (OBs) in the nucleus of hepatopancreatic epithelial cells. By in situ hybridization using different molecular probes, we tested shrimp infected with BP-type viruses collected from several geographical areas. In one shrimp, a case of double infection by 2 different BP-type viruses was noted. This has not been previously reported. The molecular probes recognized only the Pacific strain of BP. This specificity of the probe was confirmed by in situ hybridization tests with some infected shrimp collected from the Atlantic and Pacific coasts. The probes reacted only with infected shrimp obtained from the Pacific coast. These results suggest the existence of at least 2 different BP-type viruses and show that specific probes can be used to differentiate between them

Construction of a gene probe for the detection of P virus (Reoviridae) infections in decapod crustaceans.

The construction is described of a molecular probe to P virus, a double stranded RNA virus belonging to the Reoviridiae, which is an endemic pathogen of swimming crabs in British coastal waters and the Mediterranean. The probe hybridises to the P virus genome and can be easily produced in large quantities by PCR. It may be used by dot blotting or in situ hybridisation to specifically detect P virus in tissues and cells of natural or experimentally infected animals. Analyses of tissue samples with this probe show that the virus infects connective tissues of gills and hepatopancreas. This is the first gene probe to be constructed for a native viral pathogen of temperate water brachyurans and it will be useful to study virus ecology and virus-host interactions in vivo and in vitro. An understanding of these processes is essential to control and manage disease and, ultimately, to identify immune effecters capable of destroying viral pathogens. (C) 1999 Elsevier Science B.V. All rights reserved.</p