Smooth Nonlinear Optimization in Rn

Smooth Nonlinear Optimization in Rn

instance of how global investigations can be undertaken in smooth nonlinear optimization in the sense of differential geometry. Based on geodesic convexity, Chapter 7 establishes sufficient conditions for the connectedness of the ...

Author: Tamás Rapcsák

Publisher: Springer Science & Business Media

ISBN: 9781461563570

Category: Mathematics

Page: 376

View: 314

Experience gained during a ten-year long involvement in modelling, program ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in dispensable. This is the reason why I have chosen the field in question as the sphere of my research. Since in applications, mainly from among the nonconvex optimization models, the differentiable ones proved to be the most efficient in modelling, especially in solving them with computers, I started to deal with the structure of smooth optimization problems. The book, which is a result of more than a decade of research, can be equally useful for researchers and stu dents showing interest in the domain, since the elementary notions necessary for understanding the book constitute a part of the university curriculum. I in tended dealing with the key questions of optimization theory, which endeavour, obviously, cannot bear all the marks of completeness. What I consider the most crucial point is the uniform, differential geometric treatment of various questions, which provides the reader with opportunities for learning the structure in the wide range, within optimization problems. I am grateful to my family for affording me tranquil, productive circumstances. I express my gratitude to F.
Categories: Mathematics

Smooth Nonlinear Optimization in Rn

Smooth Nonlinear Optimization in Rn

This is the reason why I have chosen the field in question as the sphere of my research.

Author: Tamás Rapcsák

Publisher: Springer

ISBN: 1461379202

Category: Mathematics

Page: 376

View: 381

Experience gained during a ten-year long involvement in modelling, program ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in dispensable. This is the reason why I have chosen the field in question as the sphere of my research. Since in applications, mainly from among the nonconvex optimization models, the differentiable ones proved to be the most efficient in modelling, especially in solving them with computers, I started to deal with the structure of smooth optimization problems. The book, which is a result of more than a decade of research, can be equally useful for researchers and stu dents showing interest in the domain, since the elementary notions necessary for understanding the book constitute a part of the university curriculum. I in tended dealing with the key questions of optimization theory, which endeavour, obviously, cannot bear all the marks of completeness. What I consider the most crucial point is the uniform, differential geometric treatment of various questions, which provides the reader with opportunities for learning the structure in the wide range, within optimization problems. I am grateful to my family for affording me tranquil, productive circumstances. I express my gratitude to F.
Categories: Mathematics

Introduction to the Theory of Nonlinear Optimization

Introduction to the Theory of Nonlinear Optimization

T. Rapcsák, Smooth nonlinear optimization in Rn (Kluwer, Dordrecht, 1997). H. Ratschek and J. Rokne, New computer methods for global optimization (Ellis Horwood Limited, Chichester, 1988). B.S. Razumikhin, Physical models and ...

Author: Johannes Jahn

Publisher: Springer Nature

ISBN: 9783030427603

Category: Business & Economics

Page: 323

View: 239

This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.
Categories: Business & Economics

Modelling Computation and Optimization in Information Systems and Management Sciences

Modelling  Computation and Optimization in Information Systems and Management Sciences

Proceedings of the 4th International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences - MCO ... Rapcsák, T.: Smooth nonlinear optimization in Rn. Kluwer Academic Publishers (1997) 23.

Author: Hoai An Le Thi

Publisher: Springer Nature

ISBN: 9783030926663

Category: Artificial intelligence

Page: 413

View: 683

The proceedings consist of 34 papers which have been submitted to the 4th international conference on Modelling, Computation & Optimization in Information Systems and Management Science (MCO 2021) held on 11-13 December, 2021 at Hanoi, Vietnam. The book is composed of 3 parts: Optimization of complex systems - models and methods, Machine Learning - algorithms and applications, and Cryptography. All chapters in the books discuss theoretical and algorithmic as well as practical issues connected with modelling, computation & optimization in Information Systems and Management Science. Researchers and practitioners in related areas will find a wealth of inspiring ideas and useful tools & techniques for their own work.
Categories: Artificial intelligence

Convex Analysis and Nonlinear Optimization

Convex Analysis and Nonlinear Optimization

This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises.

Author: Jonathan M. Borwein

Publisher: Springer Science & Business Media

ISBN: 9780387295701

Category: Mathematics

Page: 316

View: 748

Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.
Categories: Mathematics

Frontiers in Functional Equations and Analytic Inequalities

Frontiers in Functional Equations and Analytic Inequalities

S. Abbaszadeh, A. Ebadian, Nonlinear integrals and Hadamard-type inequalities. Soft Comput. 22, 2843–2849 (2018) S. Abbaszadeh, ... 91–103 T. Rapcsák, Smooth Nonlinear Optimization in Rn, vol. 19 (Springer, New York, 2013) M. Sugeno, ...

Author: George A. Anastassiou

Publisher: Springer Nature

ISBN: 9783030289508

Category: Mathematics

Page: 753

View: 497

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.
Categories: Mathematics

Differentiable Optimization and Equation Solving

Differentiable Optimization and Equation Solving

Other areas of mathematical programming developed rapidly in what may fittingly be termed the Dantzig ... let f, fi, F, hi, and gj denote smooth, nonlinear functions from Rn → R: Linear Programming Model LP: minimizex∈Rn cTx s.t. aTi ...

Author: John L. Nazareth

Publisher: Springer Science & Business Media

ISBN: 9780387217888

Category: Mathematics

Page: 256

View: 603

An overview of the dramatic reorganization in reaction to N. Karmakar’s seminal 1984 paper on algorithmic linear programming in the area of algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. Aimed at readers familiar with advanced calculus and numerical analysis.
Categories: Mathematics

Variational Analysis with Applications in Optimisation and Control

Variational Analysis with Applications in Optimisation and Control

[120] T. Rapcsák, Smooth Nonlinear Optimization in Rn, Nonconvex Optimization and Its Applications, Kluwer Academic, 1997. [121] J.C. Rochet, The taxation principle and multitime Hamilton-Jacobi equations, J. Math.

Author: Savin Treanţă

Publisher: Cambridge Scholars Publishing

ISBN: 9781527537859

Category: Mathematics

Page: 186

View: 289

This book focuses on the calculus of variations and related applications which combine tools and methods from partial differential equations with geometrical techniques. More precisely, it is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. It provides the latest developments in multidimensional optimization and optimal control. With various examples and applications to complement and substantiate mathematical developments, the text is a valuable guide for researchers, engineers and students in the field of mathematics, and those working in operations research, optimal control science, artificial intelligence, management science and economics.
Categories: Mathematics

Scalar and Asymptotic Scalar Derivatives

Scalar and Asymptotic Scalar Derivatives

On a "monotonicity" method for the solution of non-linear equations in Banach spaces. ... Interior path following primal dual algorithms, Part I: Linear Programming. ... Smooth Nonlinear Optimization in Rn. Kluwer Academic, Boston.

Author: George Isac

Publisher: Springer Science & Business Media

ISBN: 9780387739885

Category: Mathematics

Page: 245

View: 498

This extremely useful book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. The text is intended for researchers and graduate students working in the fields of nonlinear analysis, Riemannian geometry and applied mathematics.
Categories: Mathematics

Encyclopedia of Optimization

Encyclopedia of Optimization

The application of the Riemannian geometry highlighted the geometric background of smooth optimization and provides it with ... Rapcsak T (1997) Smooth nonlinear optimization in Rn. Kluwer, Dordrecht | Solution Methods for Multivalued ...

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

ISBN: 9780387747583

Category: Mathematics

Page: 4646

View: 826

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Categories: Mathematics