rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Optimization
    sub title: 100 examples
  name:
    name part: Serovajsky, Simon
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    date issued: 2024
    edition: First edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: "This book is devoted to the analysis of scenarios for which the use of well-known optimization methods encounter certain difficulties. Analysing such examples allows a deeper understanding of the features of these optimization methods, including the limits of their applicability. In this way, the book seeks to stimulate further development and understanding of the theory of optimal control. The study of the presented examples makes it possible to more effectively diagnose problems that arise in the practical solution of optimal control problems, and to find ways to overcome the difficulties that have arisen"--
  table of contents: Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- PART I: MINIMIZATION OF FUNCTIONS OF ONE VARIABLE -- CHAPTER 1: Fermat theorem -- 1.1. LECTURE -- 1.1.1. Fermat theorem -- 1.1.2. Non-uniqueness of the solution of the stationary condition -- 1.1.3. Absence of function minimum points -- 1.1.4. Inapplicability of Fermat theorem -- 1.2. APPENDIX -- 1.2.1. Existence of function minimum -- 1.2.2. Uniqueness of function minimum -- 1.2.3. Tikhonov well-posedness of problems -- 1.2.4. Sufficient conditions of function minimum
  table of contents: 1.2.5. Minimization of non-smooth functions -- 1.2.6. Minimization of functions of many variables -- CHAPTER 2: Additions -- 2.1. LECTURE -- 2.1.1. Variational inequality -- 2.1.2. Dependence of the solution on parameters -- 2.1.3. Approximate solving of the stationary condition -- 2.2. APPENDIX -- 2.2.1. Sufficiency of the minimum condition in the form of variational inequalities -- 2.2.2. Lagrange multiplier method -- 2.2.3. Penalty method -- 2.2.4. Gradient methods -- 2.2.5. Hadamard well-posedness of extremum problems -- 2.2.6. Approximate solutions to the function minimization problem
  table of contents: 2.2.7. Minimization of functions of many variables -- PART II: OPTIMAL CONTROL PROBLEMS FOR SYSTEMS WITH A FREE FINITE STATE -- CHAPTER 3: Maximum principle -- 3.1. LECTURE -- 3.1.1. Statement of the optimal control problem -- 3.1.2. Maximum principle -- 3.1.3. Analytical solving of an optimal control problem -- 3.1.4. Approximate solving of an optimal control problem -- 3.2. APPENDIX -- 3.2.1. Existence of function minimum -- 3.2.2. Elimination method -- 3.2.3. Decoupling method -- 3.2.4. Algorithm Convergence for Example 3.3 -- 3.2.5. Vector optimal control problem
  table of contents: CHAPTER 4: Alternative methods -- 4.1. LECTURE -- 4.1.1. Iterative methods for solving an optimization problem -- 4.1.2. Variational inequality -- 4.1.3. Penalty method -- 4.1.4. Bellman equation -- 4.2. APPENDIX -- 4.2.1. Problem with a non-smooth functional -- 4.2.2. Non-equivalence of the variational inequality and maximum condition -- 4.2.3. Penalty method in the optimal control problem with constraints -- 4.2.4. Optimal control of a singular system -- 4.2.5. Optimal control of a singular system with constraints -- 4.2.6. Justification of the sufficient optimality condition
  table of contents: 4.2.7. Relationship between dynamic programming and the maximum principle -- 4.2.8. Applicability of Bellman optimality principle -- CHAPTER 5: Uniqueness and sufficiency -- 5.1. LECTURE -- 5.1.1. Problem statement -- 5.1.2. Maximum principle -- 5.1.3. Analysis of optimality conditions -- 5.1.4. Uniqueness of the optimal control -- 5.1.5. Completion of the analysis of optimality conditions -- 5.2. APPENDIX -- 5.2.1. Invariance of the solution under sign change -- 5.2.2. Sufficiency of the maximum principle -- 5.2.3. Properties of non-optimal solutions of the maximum principle
  note: Simon Serovajsky.
  note: Includes bibliographical references and index.
  note: Simon Serovajsky is a professor of mathematics at al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimization and optimal control theory, mathematical physics, mathematical modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.
  subject:
    topic: Mathematical optimization
  subject:
    topic: Control theory
  subject:
    topic: Optimisation mathématique
  subject:
    topic: Théorie de la commande
  subject:
    topic: MATHEMATICS / Applied
  classification: QA402.5
  classification: 515/.642
  related item:
    title info:
      title: OPTIMIZATION
    name:
      name part: SEROVAJSKY, SIMON.
    origin info:
      publisher: [Place of publication not identified] : CHAPMAN & HALL CRC, 2024
    identifier: (OCoLC)1418992954
  identifier: 9781003398585
  identifier: 1003398588
  identifier: 9781040089187
  identifier: 1040089186
  identifier: 9781040089217
  identifier: 1040089216
  identifier: 1032500077
  identifier: 9781032500072
  identifier: 9781003398585 Taylor & Francis
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: TYFRS
    record creation date: 240605
    record change date: 20241108170120.7
    record identifier: in00005526786
    language of cataloging:
      language term: eng