Handbook on Semidefinite, Conic and Polynomial Optimization


ISBN: 978-1-4614-0768-3 (Print) 978-1-4614-0769-0 (Online)

Table of contents (31 chapters)

previous Page of 2
  1. Front Matter

    Pages i-xi

  2. Chapter

    Pages 1-22

    Introduction to Semidefinite, Conic and Polynomial Optimization

  3. Theory

    1. Front Matter

      Pages 23-23

    2. Chapter

      Pages 25-60

      The Approach of Moments for Polynomial Equations

    3. Chapter

      Pages 61-75

      Algebraic Degree in Semidefinite and Polynomial Optimization

    4. Chapter

      Pages 77-112

      Semidefinite Representation of Convex Sets and Convex Hulls

    5. Chapter

      Pages 113-138

      Convex Hulls of Algebraic Sets

    6. Chapter

      Pages 139-169

      Convex Relaxations and Integrality Gaps

    7. Chapter

      Pages 171-199

      Relaxations of Combinatorial Problems Via Association Schemes

    8. Chapter

      Pages 201-218

      Copositive Programming

    9. Chapter

      Pages 219-269

      Invariant Semidefinite Programs

    10. Chapter

      Pages 271-295

      A “Joint+Marginal” Approach in Optimization

    11. Chapter

      Pages 297-337

      An Introduction to Formally Real Jordan Algebras and Their Applications in Optimization

    12. Chapter

      Pages 339-375

      Complementarity Problems Over Symmetric Cones: A Survey of Recent Developments in Several Aspects

    13. Chapter

      Pages 377-405

      Convexity and Semidefinite Programming in Dimension-Free Matrix Unknowns

    14. Chapter

      Pages 407-434

      Positivity and Optimization: Beyond Polynomials

  4. Algorithms

    1. Front Matter

      Pages 435-435

    2. Chapter

      Pages 437-454

      Self-Regular Interior-Point Methods for Semidefinite Optimization

    3. Chapter

      Pages 455-470

      Elementary Optimality Conditions for Nonlinear SDPs

    4. Chapter

      Pages 471-498

      Recent Progress in Interior-Point Methods: Cutting-Plane Algorithms and Warm Starts

    5. Chapter

      Pages 499-531

      Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems

    6. Chapter

      Pages 533-564

      Block Coordinate Descent Methods for Semidefinite Programming

    7. Chapter

      Pages 565-600

      Projection Methods in Conic Optimization

previous Page of 2