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: Convex optimization
    sub title: introductory course
  name:
    name part: Moklyachuk, Mikhail P.
    role:
      role term: creator
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    place:
      place term: London
    place:
      place term: Hoboken
    publisher: ISTE, Ltd.
    publisher: Wiley
    date issued: 2020
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (263 pages)
  abstract: This book provides easy access to the basic principles and methods for solving constrained and unconstrained convex optimization problems. Included are sections that cover: basic methods for solving constrained and unconstrained optimization problems with differentiable objective functions; convex sets and their properties; convex functions and their properties and generalizations; and basic principles of sub-differential calculus and convex programming problems.
  table of contents: Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Notations -- Introduction -- 1. Optimization Problems with Differentiable Objective Functions -- 1.1. Basic concepts -- 1.2. Optimization problems with objective functions of one variable -- 1.3. Optimization problems with objective functions of several variables -- 1.4. Constrained optimization problems -- 1.4.1. Problems with equality constraints -- 1.4.2. Problems with equality and inequality constraints -- 1.5. Exercises -- 2. Convex Sets -- 2.1. Convex sets: basic definitions
  table of contents: 2.2. Combinations of points and hulls of sets -- 2.3. Topological properties of convex sets -- 2.4. Theorems on separation planes and their applications -- 2.4.1. Projection of a point onto a set -- 2.4.2. Separation of two sets -- 2.5. Systems of linear inequalities and equations -- 2.6. Extreme points of a convex set -- 2.7. Exercises -- 3. Convex Functions -- 3.1. Convex functions: basic definitions -- 3.2. Operations in the class of convex functions -- 3.3. Criteria of convexity of differentiable functions -- 3.4. Continuity and differentiability of convex functions
  table of contents: 3.5. Convex minimization problem -- 3.6. Theorem on boundedness of Lebesgue set of a strongly convex function -- 3.7. Conjugate function -- 3.8. Basic properties of conjugate functions -- 3.9. Exercises -- 4. Generalizations of Convex Functions -- 4.1. Quasi-convex functions -- 4.1.1. Differentiable quasi-convex functions -- 4.1.2. Operations that preserve quasi-convexity -- 4.1.3. Representation in the form of a family of convex functions. -- 4.1.4. The maximization problem for quasi-convex functions -- 4.1.5. Strictly quasi-convex functions -- 4.1.6. Strongly quasi-convex functions
  table of contents: 4.2. Pseudo-convex functions -- 4.3. Logarithmically convex functions -- 4.3.1. Properties of logarithmically convex functions -- 4.3.2. Integration of logarithmically concave functions -- 4.4. Convexity in relation to order -- 4.5. Exercises -- 5. Sub-gradient and Sub-differential of Finite Convex Function -- 5.1. Concepts of sub-gradient and sub-differential -- 5.2. Properties of sub-differential of convex function -- 5.3. Sub-differential mapping -- 5.4. Calculus rules for sub-differentials -- 5.5. Systems of convex and linear inequalities -- 5.6. Exercises
  table of contents: 6. Constrained Optimization Problems -- 6.1. Differential conditions of optimality -- 6.2. Sub-differential conditions of optimality -- 6.3. Exercises -- 6.4. Constrained optimization problems -- 6.4.1. Principle of indeterminate Lagrange multipliers -- 6.4.2. Differential form of the Kuhn-Tucker theorem -- 6.4.3. Second-order conditions of optimality -- 6.5. Exercises -- 6.6. Dual problems in convex optimization -- 6.6.1. Kuhn-Tucker vector -- 6.6.2. Dual optimization problems -- 6.6.3. Kuhn-Tucker theorem for non-differentiable functions -- 6.6.4. Method of perturbations
  note: Mikhail Moklyachuk.
  note: 6.6.5. Economic interpretations of the Kuhn-Tucker vector.
  note: Includes bibliographical references and index.
  subject:
    topic: Mathematical optimization
  subject:
    topic: Convex functions
  classification: QA402.5 .M65 2020
  classification: 519.6
  related item:
    title info:
      title: Convex Optimization : Introductory Course
    name:
      name part: Moklyachuk, Mikhail.
    origin info:
      publisher: Newark : John Wiley & Sons, Incorporated, ©2021
  related item:
    title info:
      title: Oregon State monographs
      part name: Mathematics and statistics series
  identifier: 9781119804093
  identifier: 1119804094
  identifier: 1119804078
  identifier: 9781119804079
  identifier: 9781119804086
  identifier: 1119804086
  identifier: 9781786306838
  identifier: 9781119804086 Wiley
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: NhCcYBP
    record creation date: 201226
    record change date: 20260214201357.8
    record identifier: in00005618795
    language of cataloging:
      language term: eng