Bücher der Reihe SpringerBriefs in Optimization

After providing an in-depth introduction to derivative-free global optimization with various constraints, this book presents new original results from well-known experts on the subject. A primary focus of this book is the well-known class of deterministic DIRECT (DIviding RECTangle)-type algorithms. This book describes a new set of algorithms derived from newly developed partitioning, sampling, and selection approaches in the box- and generally-constrained global optimization, including extensions to multi-objective optimization. DIRECT-type optimization algorithms are discussed in terms of fundamental principles, potential, and boundaries of their applicability. The algorithms are analyzed from various perspectives to offer insight into their main features. This explains how and why they are effective at solving optimization problems. As part of this book, the authors also present several techniques for accelerating the DIRECT-type algorithms through parallelization and implementing efficient data structures by revealing the pros and cons of the design challenges involved. A collection of DIRECT-type algorithms described and analyzed in this book is available in DIRECTGO, a MATLAB toolbox on GitHub. Lastly, the authors demonstrate the performance of the algorithms for solving a wide range of global optimization problems with various constraints ranging from a few to hundreds of variables.Additionally, well-known practical problems from the literature are used to demonstrate the effectiveness of the developed algorithms. It is evident from these numerical results that the newly developed approaches are capable of solving problems with a wide variety of structures and complexity levels.Since implementations of the algorithms are publicly available, this monograph is full of examples showing how to use them and how to choose the most efficient ones, depending on the nature of the problem being solved. Therefore, many specialists, students, researchers, engineers, economists, computer scientists, operations researchers, and others will find this book interesting and helpful.

The book is devoted to the study of constrained minimization  problems on closed and convex sets in Banach spaces with a Frechet differentiable objective function. Such  problems are well studied in a  finite-dimensional space and in an infinite-dimensional Hilbert space. When the space is Hilbert there are many algorithms for solving optimization problems including the gradient projection algorithm which  is one of the most important tools in the optimization theory, nonlinear analysis and their applications. An optimization problem is described by an  objective function  and a set of feasible points. For the gradient projection algorithm each iteration consists of two steps. The first step is a calculation of a gradient of the objective function while in the second one  we calculate a projection on the feasible  set. In each of these two steps there is a computational error. In our recent research we show that the gradient projection algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. It should be mentioned that  the properties of a Hilbert space play an important role. When we consider an optimization problem in a general Banach space the situation becomes more difficult and less understood. On the other hand such problems arise in the approximation theory. The book is of interest for mathematicians working in  optimization. It also can be useful in preparation courses for graduate students.  The main feature of the book which appeals specifically to this audience is the study of algorithms for convex and nonconvex minimization problems in a general Banach space. The book is of interest for experts in applications of optimization to the approximation theory.In this book the goal is to obtain a good approximate solution of the constrained optimization problem in a general Banach space under  the presence of computational errors.  It is shown that the algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and  prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems  are studied in Chapter 3. In Chapter 4 we study  continuous   algorithms for minimization problems under the presence of computational errors. The algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and  prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems  are studied in Chapter 3. In Chapter 4 we study  continuous   algorithms for minimization problems under the presence of computational errors.

This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

Polynomial optimization have been a hot research topic for the past few years and its applications range from Operations Research, biomedical engineering, investment science, to quantum mechanics, linear algebra, and signal processing, among many others. In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications. This timely treatise will appeal to researchers and graduate students in the fields of optimization, computational mathematics, Operations Research, industrial engineering, and computer science.

Data Correcting Approaches in Combinatorial Optimization focuses on algorithmic applications of the well known polynomially solvable special cases of computationally intractable problems. The purpose of this text is to design practically efficient algorithms for solving wide classes of combinatorial optimization problems. Researches, students and engineers will benefit from new bounds and branching rules in development efficient branch-and-bound type computational algorithms. This book examines applications for solving the Traveling Salesman Problem and its variations, Maximum Weight Independent Set Problem, Different Classes of Allocation and Cluster Analysis as well as some classes of Scheduling Problems. Data Correcting Algorithms in Combinatorial Optimization introduces the data correcting approach to algorithms which provide an answer to the following questions: how to construct a bound to the original intractable problem and find which element of the corrected instance one should branch such that the total size of search tree will be minimized. The PC time needed for solving intractable problems will be adjusted with the requirements for solving real world problems.

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization.  The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful .  

Evidenced by the success of Facebook, Twitter, and LinkedIn, online social networks (OSNs) have become ubiquitous, offering novel ways for people to access information and communicate with each other. As the increasing popularity of social networking is undeniable, scalability is an important issue for any OSN that wants to serve a large number of users. Storing user data for the entire network on a single server can quickly lead to a bottleneck, and, consequently, more servers are needed to expand storage capacity and lower data request traffic per server. Adding more servers is just one step to address scalability. The next step is to determine how best to store the data across multiple servers. This problem has been widely-studied in the literature of distributed and database systems. OSNs, however, represent a different class of data systems. When a user spends time on a social network, the data mostly requested is her own and that of her friends; e.g., in Facebook or Twitter, these data are the status updates posted by herself as well as that posted by the friends. This so-called social locality should be taken into account when determining the server locations to store these data, so that when a user issues a read request, all its relevant data can be returned quickly and efficiently. Social locality is not a design factor in traditional storage systems where data requests are always processed independently. Even for today's OSNs, social locality is not yet considered in their data partition schemes. These schemes rely on distributed hash tables (DHT), using consistent hashing to assign the users' data to the servers. The random nature of DHT leads to weak social locality which has been shown to result in poor performance under heavy request loads. Data Storage for Social Networks: A Socially Aware Approach is aimed at reviewing the current literature of data storage for online social networks and discussing new methods that take into account social awareness in designing efficient data storage.

This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations. This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.

This book covers algorithm portfolios, multi-method schemes that harness optimization algorithms into a joint framework to solve optimization problems.

Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems.

Students and researchers in engineering and optimization interested in optimization methods for controller tuning will utilize this book to apply optimization algorithms to controller tuning, to choose the most suitable optimization algorithm for a specific application, and to develop new optimization techniques for controller tuning.

The discussion takes into consideration the fact that for every algorithm its iteration consists of several steps and that computational errors for different steps are different, in general.

The main topics covered in this book are: chrematistics of social networks, modeling of social influence propagation, popular research problems in social influence analysis such as influence maximization, rumor blocking, rumor source detection, and multiple social influence competing.

This book is devoted to the study of optimal control problems arising in forest management, an important and fascinating topic in mathematical economics studied by many researchers over the years.

This volume brings together the main results in the field of Bayesian Optimization (BO), focusing on the last ten years and showing how, on the basic framework, new methods have been specialized to solve emerging problems from machine learning, artificial intelligence, and system optimization.

Specific nature-inspired algorithms include: swarm intelligence, ant colony optimization, particle swarm optimization, bee-inspired algorithms, bat algorithm, firefly algorithm, and cuckoo search.

Numerical minimization of an objective function is analyzed in this book to understand solution algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical minimization as a repeated application of an iteration mapping. Ideas from numerical variational analysis are extended to define and explore notions of continuity and differentiability of multiset-mappings, and prove a fixed-point theorem for iteration mappings. Concepts from dynamical systems are utilized to develop notions of basin size and basin entropy. Simulations to estimate basins of attraction, to measure and classify basin size, and to compute basin are included to shed new light on convergence behavior in numerical minimization.Graduate students, researchers, and practitioners in optimization and mathematics who work theoretically to develop solution algorithms will find this book a useful resource.

This book explores the updated version of the GLOBAL algorithm which contains improvements for a local search algorithm and new Java implementations.

This book presents an up-to-date review of modeling and optimization approaches for location problems along with a new bi-level programming methodology which captures the effect of competition of both producers and customers on facility location decisions.

the first has to do with the possibility of determining the input-output system from its natural state set and the second deals with differentiability properties involving the natural state inherited from the input-output system, including differentiability of the natural state and natural state trajectories.

This book combines game theory and complex networks to examine intentional technological risk through modeling. This model manages the risk of succumbing to a digital attack and assesses an attack from the following three variables: income obtained, expense needed to carry out an attack, and the potential consequences for an attack.

This book defines and develops the generalized adjoint of an input-output system. For a space of input-output systems, a generalized adjoint map from this space of systems to the space of generalized adjoints is defined.