A Feasible Method for Optimization with Orthogonality Constraints

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Ansary Karbasi, Saeed | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46056 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezameddin
Abstract:
Minimizing problems with either orthogonal or spherical constraints has a great number of applications in combinatorial optimization, polynomial optimization,eigenvalue problem, estimation to the nearest correlation between matrices of low rank, etc. Solving this kind of problem is hard, because feasible spaces for constraints are non-convex, and solving them is very costly as well. For confronting with this issue, The Cayley transform is used for keeping constraints,and, based on this technique, a smooth curve algorithm with low flop is compared with some algorithms based on is projections and geodesics . Efficiency of the algorithm, recently in introduced the literature, is proved on a considerable set of problems. Specifically, the method solves an decomposed formulation for released SDP in exactly. The algorithm provides better results for polynomial optimization, estimation to the nearest correlation between matrices of low rank, and eigenvalue problem than other traditional algorithms. In allocation problem, a gap of 1.004 for the best solution is found in approximately 5 minutes for the big problem of tai256c in QAPLIB on an ordinary laptop
Keywords:
Orthogonality Constrain ; Spherical Constrain ; Stiefel Manifold ; Cayley Transformation ; Curvilinear Seareh