International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Generalized Maximum Entropy, Convexity and Machine Learning

This thesis identifies and extends techniques that can be linked to the principle of maximum entropy (maxent) and applied to parameter estimation in machine learning and statistics. Entropy functions based on deformed logarithms are used to construct Bregman divergences, and together these represent a generalization of relative entropy. The framework is analyzed using convex analysis to charac- terize generalized forms of exponential family distributions. Various connections to the existing machine learning literature are discussed and the techniques are applied to the problem of non-negative matrix factorization (NMF)

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

Progress in Nondifferentiable Optimization

This volume grew out of the second meeting on nondifferentiable optimization, a field whose most important applications lie in treating problems of decision-making under uncertainty. Since the first meeting, held in 1977, new results were obtained in the theory of optimality conditions, and there was more understanding of the relationships between various classes of nondifferentiable functions. All of these new developments were discussed at the meeting, the reports presented by the participants covering the theory of generalized differentiability, optimality conditions, and the numerical testing and applications of algorithms. After the meeting the participants prepared extended versions of their contributions; these revised papers form the core of this volume, which also contains a bibliography of over 300 references to published work on nondifferentiable optimization, prepared by the editor

Efficient algorithms for distributed learning, optimization and belief systems over networks

A distributed system is composed of independent agents, machines, processing units, etc., where interactions between them are usually constrained by a network structure. In contrast to centralized approaches where all information and computation resources are available at a single location, agents on a distributed system can only use locally available information. The particular flexibilities induced by a distributed structure make it suitable for large-scale problems involving large quantities of data. Specifically, the increasing amount of data generated by inherently distributed systems such as social media, sensor networks, and cloud-based databases has brought considerable attention to distributed data processing techniques on several fronts of applied and theoretical machine learning, robotics, resource allocation, among many others. As a result, much effort has been put into the design of efficient distributed algorithms that take into account the communication constraints and make coordinated decisions in a fully distributed manner. In this dissertation, we focus on the principled design and analysis of distributed algorithms for optimization, learning and belief systems over networks. Particularly, we are interested in the non-asymptotic analysis of various distributed algorithms and the explicit influence of the topology of the network they ought to be solved over. Initially, we analyze a recently proposed model for opinion dynamics in belief systems with logic constraints. Opinion dynamics are a natural model for a distributed system and serve as an introductory topic for the further study of learning and optimization over networks. We assume there is an underlying structure of social relations, represented by a social network, and people in this social group interact by exchanging opinions about a number of truth statements. We analyze, from a graph-theoretic point of view, this belief system when a set of logic constraints relate the opinions on the several topics being discussed. We provide novel graph-theoretic conditions for convergence, explicit estimates of the convergence rate and the limiting value of the opinions for all agents in the network in terms of the topology of the social structure of the agents and the topology induced by the set of logic constraints. We derive explicit dependencies for a number of well-known graph topologies. We then shift our attention to the distributed learning problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of network-wide observations using the local information only. Again, we assume there is an underlying network that defines the communication constraints between the agents and derive explicit, non-asymptotic, and geometric convergence rates for the concentration of beliefs on the optimal parameter. For the case of having a finite number of hypotheses, we propose distributed learning algorithms for time-varying undirected graphs, time-varying directed graphs and a new acceleration scheme for fixed undirected graphs. For each of the network structures, we present explicit dependencies for the worst case network topology. Furthermore, we extend these belief concentration results to hypotheses sets being a compact subset of the real numbers, for a simplified static undirected network assumption. Moreover, we present a generic distributed parameter estimation algorithm for observational models belonging to the exponential family of distributions. We further extend the distributed mean estimation from Gaussian observations to time-varying directed networks. The graph-theoretical analysis of belief systems with logic constraints and the distributed learning for cooperative inference are specific instances of convex optimization problems where the objective function is decomposable as the sum of convex functions. Particularly, these problems assume each of the summands is held by a node on a graph and agents are oblivious to the network topology. As a final object of interest, we study the optimality of first-order distributed optimization algorithms for general convex optimization problems. We focus on understanding the fundamental limits induced by the distributed networked structure of the problem and how it compares with the hypothetical case of having centralized computations available. We show that for large classes of convex optimization problems, we can design optimal algorithms that can be executed over a network in a distributed manner while matching lower complexity bounds of their centralized counterparts with an additional iteration cost that depends on the network structure. We design optimal distributed algorithms for various convexity and smoothness properties that can be executed over arbitrary fixed, connected and undirected graphs. Furthermore, we explore the application of these distributed algorithms to the problem of distributed computation of Wasserstein barycenters of finite distributions. Finally, we discuss some future directions of research for the design and analysis of distributed algorithms, both from theoretical and applied perspectives

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio