Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.

In many decision problems, e.g. from the area of production and logistics manage ment, the evaluation of alternatives and the determination of an optimal or at least suboptimal solution is an important but dif?cult task. For most such problems no ef?cient algorithm is known and classical approaches of Operations Research like Mixed Integer Linear Programming or Dynamic Pro gramming are often of limited use due to excessive computation time. Therefore, dedicated heuristic solution approaches have been developed which aim at providing good solutions in reasonable time for a given problem. However, such methods have two major drawbacks: First, they are tailored to a speci?c prob lem and their adaption to other problems is dif?cult and in many cases even impos sible. Second, they are typically designed to "build" one single solution in the most effective way, whereas most decision problems have a vast number of feasible solu tions. Hence usually the chances are high that there exist better ones. To overcome these limitations, problem independent search strategies, in particular metaheuris tics, have been proposed. This book provides an elementary step by step introduction to metaheuristics focusing on the search concepts they are based on. The ?rst part demonstrates un derlying concepts of search strategies using a simple example optimization problem.

In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic geometry for studying polynomial optimization problems. Classes of generic problems are defined in a simple and elegant manner by using only the two basic (and relatively simple) notions of Newton polyhedron and non-degeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.Explanations focus on critical points and tangencies of polynomial optimization, Hoelderian error bounds for polynomial systems, Frank-Wolfe-type theorem for polynomial programs and well-posedness in polynomial optimization. It then goes on to look at optimization for the different types of polynomials. Through this text graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semi-algebraic geometry in optimization.

This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.

The aim of this book is to furnish the reader with a rigorous and detailed exposition of the concept of control parametrization and time scaling transformation. It presents computational solution techniques for a special class of constrained optimal control problems as well as applications to some practical examples. The book may be considered an extension of the 1991 monograph A Unified Computational Approach Optimal Control Problems, by K.L. Teo, C.J. Goh, and K.H. Wong. This publication discusses the development of new theory and computational methods for solving various optimal control problems numerically and in a unified fashion. To keep the book accessible and uniform, it includes those results developed by the authors, their students, and their past and present collaborators. A brief review of methods that are not covered in this exposition, is also included. Knowledge gained from this book may inspire advancement of new techniques to solve complex problems that arise in the future. This book is intended as reference for researchers in mathematics, engineering, and other sciences, graduate students and practitioners who apply optimal control methods in their work. It may be appropriate reading material for a graduate level seminar or as a text for a course in optimal control.

This volume consists of selected essays by participants of the workshop Control at Large Scales: Energy Markets and Responsive Grids held at the Institute for Mathematics and its Applications, Minneapolis, Minnesota, U.S.A. from May 9-13, 2016. The workshop brought together a diverse group of experts to discuss current and future challenges in energy markets and controls, along with potential solutions. The volume includes chapters on significant challenges in the design of markets and incentives, integration of renewable energy and energy storage, risk management and resilience, and distributed and multi-scale optimization and control. Contributors include leading experts from academia and industry in power systems and markets as well as control science and engineering. This volume will be of use to experts and newcomers interested in all aspects of the challenges facing the creation of a more sustainable electricity infrastructure, in areas such as distributed and stochastic optimization and control, stability theory, economics, policy, and financial mathematics, as well as in all aspects of power system operation.

This book highlights recent developments in multidimensional data visualization, presenting both new methods and modifications on classic techniques. Throughout the book, various applications of multidimensional data visualization are presented including its uses in social sciences (economy, education, politics, psychology), environmetrics, and medicine (ophthalmology, sport medicine, pharmacology, sleep medicine).

The book provides recent research results in optimization-based visualization. Evolutionary algorithms and a two-level optimization method, based on combinatorial optimization and quadratic programming, are analyzed in detail. The performance of these algorithms and the development of parallel versions is discussed.

The encorporation of new visualization techniques to improve the capabilies of artificial neural networks (self-organizing maps, feed-forward networks) is also discussed.

The book includes over 100 detailed images presenting examples of the different visualization techniques that are presented.

This book is intended for scientists and researchers in any field of study where complex and multidimensional data must be represented visually.

This book describes the interplay of mechanics, electronics, electrotechnics, automation and biomechanics. It provides a broad overview of mechatronics systems ranging from modeling and dimensional analysis, and an overview of magnetic, electromagnetic and piezo-electric phenomena. It also includes the investigation of the pneumo-fluid-mechanical, as well as electrohydraulic servo systems, modeling of dynamics of an atom/particle embedded in the magnetic field, integrity aspects of the Maxwell's equations, the selected optimization problems of angular velocity control of a DC motor subjected to chaotic disturbances with and without stick-slip dynamics, and the analysis of a human chest adjacent to the elastic backrest aimed at controlling force to minimize relative compression of the chest employing the LQR.This book provides a theoretical background on the analysis of various kinds of mechatronics systems, along with their computational analysis, control, optimization as well as laboratory investigations.

Modeling, Simulation, and Optimization of Supply Chains is an up-to-date introduction to the mathematical theory of supply chains, which focuses on those supply chain networks which are described by partial differential equations. The book discusses modeling of complex supply networks as well as their mathematical theory. In addition, the authors investigate the optimization of some of the discussed models and present the analytical and numerical results on optimization problems. Practical examples demonstrate the applicability of the presented approaches. The book provides an introduction to the topic and also explores the more advanced theoretical and numerical background. Graduate students and researchers, who wish to stay abreast of the latest developments in this field, will be interested in this book; it may be used to teach advanced courses on modeling of physical phenomena as well as introductory courses on supply chain theory.

This volume presents selected contributions by top researchers in the field of operations research, originating from the XVI Congress of APDIO. It provides interesting findings and applications of operations research methods and techniques in a wide variety of problems. The contributions address complex real-world problems, including inventory management with lateral transshipments, sectors and routes in solid-waste collection and production planning for perishable food products. It also discusses the latest techniques, making the volume a valuable tool for researchers, students and practitioners who wish to learn about current trends. 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, as well as job scheduling problems. This biennial conference, organized by APDIO, the Portuguese Association of Operational Research, held in Braganca, Portugal, in June 2013, presented a perfect opportunity to discuss the latest development in this field and to narrow the gap between academic researchers and practitioners.

This book features a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in B ethlehem, Pennsylvania, USA between August 16-18, 2017. The conference brought together a diverse group of researchers and practitioners working on both theoretical and practical aspects of continuous and discrete optimization. Topics covered include algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and address the application of deterministic andstochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The selected contributions in this book illustrate the broad diversity of ideas discussed at the meeting.

Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering.Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes 'P' (polynomial time) and 'NP' (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.

"Impulsive Control in Continuous and Discrete-Continuous Systems" is an up-to-date introduction to the theory of impulsive control in nonlinear systems. This is a new branch of the Optimal Control Theory, which is tightly connected to the Theory of Hybrid Systems. The text introduces the reader to the interesting area of optimal control problems with discontinuous solutions, discussing the application of a new and effective method of discontinuous time-transformation. With a large number of examples, illustrations, and applied problems arising in the area of observation control, this book is excellent as a textbook or reference for a senior or graduate-level course on the subject, as well as a reference for researchers in related fields.

Thanks to recent advancements, optimization is now recognized as a crucial component in research and decision-making across a number of fields. Through optimization, scientists have made tremendous advances in cancer treatment planning, disease control, and drug development, as well as in sequencing DNA, and identifying protein structures. Optimization in Medicine and Biology provides researchers with a comprehensive, single-source reference that will enable them to apply the very latest optimization techniques to their work. With contributions from pioneering international experts this volume integrates strong foundational theory, good modeling techniques, and efficient and robust algorithms with relevant applications Divided into two sections, the first begins with mathematical programming techniques for medical decision making processes and demonstrates their application to optimizing pediatric vaccine formularies, kidney paired donation, and the cost-effectiveness of HIV programs. It also presents recent advances in cancer treatment planning models and solution algorithms, including three-dimensional conventional conformal radiation therapy (3DCRT), intensity modulated radiation therapy (IMRT), tomotherapy, and proton therapy. Part two focuses on optimization in biology and discusses computational algorithms for genomic analysis; probe design and selection, properties of probes, and various algorithms and software packages to aid in probe selection and design. Subsequent chapters introduce a new dihedral angle measure for protein secondary prediction, and an optimization approach for tumor virotherapy with recombinant measles viruses. The editors include a short tutorial appendix on Integer Programming (IP). Highlighting the most recent advances in optimization techniques for solving complex problems in medical research, this book facilitates strong collaborative environments among optimization researchers and medical professionals for future medical research.

This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.

This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

This self-contained monograph presents the reader with an authoritative view of Continuous Optimization, an area of mathematical optimization that has experienced major developments during the past 40 years. The book contains results which have not yet been covered in a systematic way as well as a summary of results on NR theory and methods developed over the last several decades. The readership is aimed to graduate students in applied mathematics, computer science, economics, as well as researchers working in optimization and those applying optimization methods for solving real life problems. Sufficient exercises throughout provide graduate students and instructors with practical utility in a two-semester course in Continuous Optimization. The topical coverage includes interior point methods, self-concordance theory and related complexity issues, first and second order methods with accelerated convergence, nonlinear rescaling (NR) theory and exterior point methods, just to mention a few. The book contains a unified approach to both interior and exterior point methods with emphasis of the crucial duality role. One of the main achievements of the book shows what makes the exterior point methods numerically attractive and why. The book is composed in five parts. The first part contains the basics of calculus, convex analysis, elements of unconstrained optimization, as well as classical results of linear and convex optimization. The second part contains the basics of self-concordance theory and interior point methods, including complexity results for LP, QP, and QP with quadratic constraint, semidefinite and conic programming. In the third part, the NR and Lagrangian transformation theories are considered and exterior point methods are described. Three important problems in finding equilibrium are considered in the fourth part. In the fifth and final part of the book, several important applications arising in economics, structural optimization, medicine, statistical learning theory, and more, are detailed. Numerical results, obtained by solving a number of real life and test problems, are also provided.

Experimental Design and Process Optimization delves deep into the design of experiments (DOE). The book includes Central Composite Rotational Design (CCRD), fractional factorial, and Plackett and Burman designs as a means to solve challenges in research and development as well as a tool for the improvement of the processes already implemented. Appropriate strategies for 2 to 32 factors are covered in detail in the book. The book covers the essentials of statistical science to assist readers in understanding and applying the concepts presented. It also presents numerous examples of applications using this methodology. The authors are not only experts in the field but also have significant practical experience. This allows them to discuss the application of the theoretical aspects discussed through various real-world case studies.

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.

This book presents select peer-reviewed papers presented at the International Conference on Numerical Optimization in Engineering and Sciences (NOIEAS) 2019. The book covers a wide variety of numerical optimization techniques across all major engineering disciplines like mechanical, manufacturing, civil, electrical, chemical, computer, and electronics engineering. The major focus is on innovative ideas, current methods and latest results involving advanced optimization techniques. The contents provide a good balance between numerical models and analytical results obtained for different engineering problems and challenges. This book will be useful for students, researchers, and professionals interested in engineering optimization techniques.

This handbook gathers state-of-the-art research on optimization problems in power distribution systems, covering classical problems as well as the challenges introduced by distributed power generation and smart grid resources. It also presents recent models, solution techniques and computational tools to solve planning problems for power distribution systems and explains how to apply them in distributed and variable energy generation resources. As such, the book therefore is a valuable tool to leverage the expansion and operation planning of electricity distribution networks.

This book, compiles, presents, and explains the most important meta-heuristic and evolutionary optimization algorithms whose successful performance has been proven in different fields of engineering, and it includes application of these algorithms to important engineering optimization problems. In addition, this book guides readers to studies that have implemented these algorithms by providing a literature review on developments and applications of each algorithm. This book is intended for students, but can be used by researchers and professionals in the area of engineering optimization.

Optimization, simulation and control play an increasingly important role in science and industry. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace.

This volume brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. The book is composed of invited contributions by experts from around the world who work to develop and apply new optimization, simulation and control techniques either at a theoretical level or in practice. Some key topics presented include: equilibrium problems, multi-objective optimization, variational inequalities, stochastic processes, numerical analysis, optimization in signal processing, and various other interdisciplinary applications.

This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization, simulation and control can be applied.

This book presents a study to determine the current limitations in the area of Photovoltaics (PV) as a source of renewable energy and proposes strategies to overcome them by applying optimization approaches in three main areas, namely related to photovoltaic solar cells, modules, and systems. These include grid metallization design of Si-based solar cells and modules; cost-effectiveness analysis between Si-based monofacial and bifacial grid-connected PV systems; optimal diesel replacement strategy for the progressive introduction of PV and batteries; dispatch strategy optimization for PV hybrid systems in real time. The novelty of the work presented in this book is of high interest to the scientific community but also to the PV manufacturers, installation companies, and investors.

Constrained optimization is a challenging branch of operations research that aims to create a model which has a wide range of applications in the supply chain, telecommunications and medical fields. As the problem structure is split into two main components, the objective is to accomplish the feasible set framed by the system constraints. The aim of this book is expose optimization problems that can be expressed as graphs, by detailing, for each studied problem, the set of nodes and the set of edges. This graph modeling is an incentive for designing a platform that integrates all optimization components in order to output the best solution regarding the parameters' tuning. The authors propose in their analysis, for optimization problems, to provide their graphical modeling and mathematical formulation and expose some of their variants. As a solution approaches, an optimizer can be the most promising direction for limited-size instances. For large problem instances, approximate algorithms are the most appropriate way for generating high quality solutions. The authors thus propose, for each studied problem, a greedy algorithm as a problem-specific heuristic and a genetic algorithm as a metaheuristic.