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The new edition contains modifications and additions which take into account recent developments in the field. From the reviews of earlier editions: "The book is clearly written and lucidly structured. In particular, the used notations are thoroughly defined, the diverse ideas are well explained, and the results are beautifully motivated." (ZOR. Methods and Models of Operations Research). This book develops a systematic and unifying approach to the most important classes of constrained global optimization and their solution techniques. The main problem classes treated are concave minimization, reverse convex and d. c. programming, Lipschitz and continuous optimization, and systems of equations and inequalities.
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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact
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Programmation mathematique --- Programmation mathematique --- Programmation mathematique --- Global optimization --- Programmation non lineaire --- Programmation entiere --- Methodes numeriques --- Deterministic approaches --- Programmation mathematique --- Programmation mathematique --- Programmation mathematique --- Global optimization --- Programmation non lineaire --- Programmation entiere --- Methodes numeriques --- Deterministic approaches
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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact
Science: general issues --- molecular geometry search --- fitting potential energy functions --- spectral assignment --- global optimization algorithms --- energy landscapes --- molecular geometry search --- fitting potential energy functions --- spectral assignment --- global optimization algorithms --- energy landscapes
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This book is an introduction to nonlinear programming. It deals with the theoretical foundations and solution methods, beginning with the classical procedures and reaching up to "modern" methods like trust region methods or procedures for nonlinear and global optimization. A comprehensive bibliography including diverse web sites with information about nonlinear programming, in particular software, is presented. Without sacrificing the necessary mathematical rigor, excessive formalisms are avoided. Several examples, exercises with detailed solutions, and applications are provided, making the text adequate for individual studies. The book is written for students from the fields of applied mathematics, engineering, economy, and computation.
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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact
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Simplicial Global Optimization is centered on deterministic covering methods partitioning feasible region by simplices. This book looks into the advantages of simplicial partitioning in global optimization through applications where the search space may be significantly reduced while taking into account symmetries of the objective function by setting linear inequality constraints that are managed by initial partitioning. The authors provide an extensive experimental investigation and illustrates the impact of various bounds, types of subdivision, strategies of candidate selection on the performance of algorithms. A comparison of various Lipschitz bounds over simplices and an extension of Lipschitz global optimization with-out the Lipschitz constant to the case of simplicial partitioning is also depicted in this text. Applications benefiting from simplicial partitioning are examined in detail such as nonlinear least squares regression and pile placement optimization in grillage-type foundations. Researchers and engineers will benefit from simplicial partitioning algorithms such as Lipschitz branch and bound, Lipschitz optimization without the Lipschitz constant, heuristic partitioning presented. This book will leave readers inspired to develop simplicial versions of other algorithms for global optimization and even use other non-rectangular partitions for special applications.
Mathematics. --- Combinatorial analysis. --- Nonconvex programming. --- Global optimization --- Non-convex programming --- Combinatorics --- Math --- Applied mathematics. --- Engineering mathematics. --- Operations research. --- Management science. --- Combinatorics. --- Operations Research, Management Science. --- Applications of Mathematics. --- Programming (Mathematics) --- Algebra --- Mathematical analysis --- Science --- Engineering --- Engineering analysis --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mathematics --- Mathematical optimization.
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This book presents a comprehensive description of theory, algorithms and software for solving nonconvex mixed integer nonlinear programs (MINLP). The main focus is on deterministic global optimization methods, which play a very important role in integer linear programming, and are used only recently in MINLP. The presented material consists of two parts. The first part describes basic optimization tools, such as block-separable reformulations, convex and Lagrangian relaxations, decomposition methods and global optimality criteria. Some of these results are presented here for the first time. The second part is devoted to algorithms. Starting with a short overview on existing methods, deformation, rounding, partitioning and Lagrangian heuristics, and a branch-cut-and-price algorithm are presented. The algorithms are implemented as part of an object-oriented library, called LaGO. Numerical results on several mixed integer nonlinear programs are reported to show abilities and limits of the proposed solution methods. The book contains many illustrations and an up-to-date bibliography. Because of the emphasis on practical methods, as well as the introduction into the basic theory, it is accessible to a wide audience and can be used both as a research as well as a graduate text.
Nonconvex programming. --- Nonlinear programming. --- Integer programming. --- Programming (Mathematics) --- Global optimization --- Non-convex programming --- Nonconvex programming --- Nonlinear programming --- Integer programming --- Computer science. --- Mathematics. --- Algorithms. --- Math Applications in Computer Science. --- Applications of Mathematics. --- Computational Science and Engineering. --- Programming Techniques. --- Algorism --- Algebra --- Arithmetic --- Math --- Science --- Informatics --- Foundations --- Computer science—Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Computer programming. --- Computers --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Computer mathematics --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Programming
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.
complexity --- cuckoo search --- magnetic resonance imaging --- fractional calculus --- musical signal --- pinning synchronization --- Fourier transform --- optimal randomness --- fractional-order system --- Mittag-Leffler function --- meaning --- parameter --- diffusion-wave equation --- anomalous diffusion --- Laplace transform --- time-varying delays --- mass absorption --- swarm-based search --- fractional --- adaptive control --- time series --- Hurst exponent --- fractional derivative --- control --- PID --- global optimization --- reaction–diffusion terms --- audio signal processing --- Caputo derivative --- harmonic impact --- fractional complex networks --- heavy-tailed distribution --- impulses --- long memory --- linear prediction
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In the field of nondifferentiable nonconvex optimization, one of the most intensely investigated areas is that of optimization problems involving multivalued mappings in constraints or as the objective function. This book focuses on the tremendous development in the field that has taken place since the publication of the most recent volumes on the subject. The new topics studied include the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the coderivative of Mordukhovich), the opening of new applications (e.g., the calibration of water supply systems), or the elaboration of new solution algorithms (e.g., smoothing methods). The book is divided into three parts. The focus in the first part is on bilevel programming. The chapters in the second part contain investigations of mathematical programs with equilibrium constraints. The third part is on multivalued set-valued optimization. The chapters were written by outstanding experts in the areas of bilevel programming, mathematical programs with equilibrium (or complementarity) constraints (MPEC), and set-valued optimization problems. Audience This book is intended for researchers, graduate students and practitioners in the fields of applied mathematics, operations research, and economics.
Nonlinear programming. --- Nonconvex programming. --- Set-valued maps. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Many-valued mappings --- Mappings, Point-to-set --- Maps, Set-valued --- Multi-valued mappings --- Multivalued mappings --- Point-to-set mappings --- Mappings (Mathematics) --- Selection theorems --- Global optimization --- Non-convex programming --- Programming (Mathematics) --- Mathematical optimization. --- Optimization. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of
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