On Solving Selected Nonlinear Integer Programming Problems in Data Mining, Computational Biology, and Sustainability

This thesis consists of three essays concerning the use of optimization techniques to solve four problems in the fields of data mining, computational biology, and sustainable energy devices. To the best of our knowledge, the particular problems we discuss have not been previously addressed using optimization, which is a specific contribution of this dissertation. In particular, we analyze each of the problems to capture their underlying essence, subsequently demonstrating that each problem can be modeled as a nonlinear (mixed) integer program. We then discuss the design and implementation of solution techniques to locate optimal solutions to the aforementioned problems. Running throughout this dissertation is the theme of using mixed-integer programming techniques in conjunction with context-dependent algorithms to identify optimal and previously undiscovered underlying structure

Global Optimality in Representation Learning

A majority of data processing techniques across a wide range of technical disciplines require a representation of the data that is meaningful for the task at hand in order to succeed. In some cases one has enough prior knowledge about the problem that a fixed transformation of the data or set of features can be pre-calculated, but for most challenging problems with high dimensional data, it is often not known what representation of the data would give the best performance. To address this issue, the field of representation learning seeks to learn meaningful representations directly from data and includes methods such as matrix factorization, tensor factorization, and neural networks. Such techniques have achieved considerable empirical success in many fields, but common to a vast majority of these approaches are the significant disadvantages that 1) the associated optimization problems are typically non-convex due to a multilinear form or other convexity destroying transformation and 2) one is forced to specify the size of the learned representation a priori. This thesis presents a very general framework which allows for the mathematical analysis of a wide range of non-convex representation learning problems. The framework allows the derivation of sufficient conditions to guarantee that a local minimizer of the non-convex optimization problem is a global minimizer and that from any initialization it is possible to find a global minimizer using a purely local descent algorithm. Further, the framework also allows for a wide range of regularization to be incorporated into the model to capture known features of data and to adaptively fit the size of the learned representation to the data instead of defining it a priori. Multiple implications of this work are discussed as they relate to modern practices in deep learning, and the advantages of the approach are demonstrated in applications of automated spatio-temporal segmentation of neural calcium imaging data and reconstructing hyperspectral image volumes from compressed measurements

Livro de atas do XVI Congresso da Associação Portuguesa de Investigação Operacional

Fundação para a Ciência e Tecnologia - FC

Operational Research IO2017, Valença, Portugal, June 28-30

This proceedings book presents selected contributions from the XVIII Congress of APDIO (the Portuguese Association of Operational Research) held in Valença on June 28–30, 2017. Prepared by leading Portuguese and international researchers in the field of operations research, it covers a wide range of complex real-world applications of operations research methods using recent theoretical techniques, in order to narrow the gap between academic research and practical applications. Of particular interest are the applications of, nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management, and lot sizing and job scheduling problems. In most chapters, the problems, methods and methodologies described are complemented by supporting figures, tables and algorithms. The XVIII Congress of APDIO marked the 18th installment of the regular biannual meetings of APDIO – the Portuguese Association of Operational Research. The meetings bring together researchers, scholars and practitioners, as well as MSc and PhD students, working in the field of operations research to present and discuss their latest works. The main theme of the latest meeting was Operational Research Pro Bono. Given the breadth of topics covered, the book offers a valuable resource for all researchers, students and practitioners interested in the latest trends in this field.info:eu-repo/semantics/publishedVersio