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A Trust Region Method for Solving Semidefinite Programs

Nazari, Parvin | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47624 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi-Amiri, Nezamoddin
  7. Abstract:
  8. In this thesis, we exmine a group of optimization methods called trust region methods for solving semidefinite programming problems. Nowadays, many application problems can be cast as semidefinite programming and problems with very large size are encountered every year. So, having a powerful method for solving such problems is very important. Trust region approach present a new scheme for constructing efficient algorithms to solve semidefinite programming problems.When using interior point methods for solving semidefinite programs (SDPs), one needs to solve a system of linear equations at every iteration. For large problems, solving the system of linear equations can be very expensive. In this thesis, our aim is to describe a trust region method, recently proposed in the literature for solving semidefinite programming problems. At each iteration, we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations.The convergence of this algorithm is established. Finally, the method is implemented and tested with MATLAB codes. We compare our obtained results on various test problems with the results obtained by some other existing algorithms. Our numerical results confirm the efficiency of the algorithm
  9. Keywords:
  10. Semidefinite Programming ; Global Convergence ; Freshet Differentiation ; Trust Region

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