Welcome to the geometric optimization webpage!

Geometric optimization refers broadly to the subject of optimizing a cost function subject to the parameters satisfying certain geometric properties. One familiar example is manifold optimization, where the geometric structure is that of a Riemannian or Finslerian manifold. Another key example is Conic geometric optimization, which includes geometric programming in its simplest (commutative) incarnation.

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Relevant Papers

  1. On the matrix square root and geometric optimization 🍒 🍀
          Suvrit Sra
         (Version: Jul 2015)
         
    @Article{sraRoot,
    author = {Suvrit Sra},
    title = {{On the matrix square root and geometric optimization}},
    journal = {arXiv:1507.08366},
    year = {2015},
    note = {\it Preprint}
    }
    

  2. Riemannian dictionary learning and sparse coding for positive definite matrices 🍒
          Anoop Cherian, Suvrit Sra
         (Version of: July 2015)
         
    @Article{cheSra15,
    author = {Anoop Cherian and Suvrit Sra},
    title = {{Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices}},
    journal = {arXiv:1507.02772},
    mon     = {Jul.},
    year = {2015},
    }
    

  3. Inference and mixture modelling with the Elliptical Gamma Distribution 🍒
          Reshad Hosseini, Suvrit Sra, Lucas Theis, Matthias Bethge
         (Submitted: Oct 2014; Revised: Jul. 2015)
         
    
    @Article{hoSra14,
    author = {Reshad Hosseini and Suvrit Sra and L. Theis and M. Bethge},
    title = {Statistical inference with the Elliptical Gamma Distribution},
    journal = {arXiv:1410.4812},
    year = {2014},
    note = {{\it Submitted}},
    }
    

  4. Positive Definite Matrices and the S-Divergence 🍀
          Suvrit Sra
         Proceedings of the American Mathematical Society (to appear)
         
    @Article{srasdiv,
    author = {Suvrit Sra},
    title = {{Positive Definite Matrices and the S-Divergence}},
    journal = {Proceedings of the American Mathematical Society},
    year = {2015},
    mon  = {Sep}
    note = {arXiv:1110.1773v4}
    }
    


  5. Manifold optimization for mixture modeling 🍒
          Reshad Hosseini, Suvrit Sra
         Advances in Neural Information Processing Systems (NIPS 2015) (to appear)
         
    @Article{hosSra15b,
    author = {Reshad Hosseini and Suvrit Sra},
    title = {{Manifold optimization for mixture modeling}},
    journal = {arXiv:1506.07677},
    year = {2015},
    note = {\it Submitted}
    }
    

  6. Hlawka-Popoviciu inequalities on positive definite tensors 🍀
          Wolfgang Berndt, Suvrit Sra
          Linear Algebra and its Applications    (Accept: Feb 2015)
         
    @Article{berSra15,
    author = {Wolfgang Berndt and Suvrit Sra},
    title = {{Hlawka-Popoviciu inequalities on positive definite tensors}},
    journal = {Linear Algebra and its Applications},
    volume = {486},
    number = {1},
    pages = {317--327},
    year = {2015},
    note = {arXiv:1411.0065}
    }
    

  7. Fixed-point algorithms for learning determinantal point processes 🍒
          Zelda Mariet, Suvrit Sra
          International Conf. on Machine Learning (ICML 2015);
         
    @Inproceedings{marSra15,
    author = {Zelda Mariet and Suvrit Sra},
    title = {{Fixed-point algorithms for learning determinantal point processes}},
    booktitle = {International Conference on Machine Learning (ICML)},
    mon     = {Jun},
    year = {2015},
    }
    

  8. Conic geometric optimisation on the manifold of positive definite matrices 🍀 🍒
          Suvrit Sra, Reshad Hosseini
          SIAM J. Optimization (SIOPT)   (Jan 2015)
         
    @Article{sraHo15,
    author = {Suvrit Sra and Reshad Hosseini},
    title = {{Conic Geometric Optimization on the Manifold of Positive Definite Matrices}},
    volume = {25},
    number = {1},
    pages  = {713--739},
    journal = {SIAM J. Optimization (SIOPT)},
    year = {2015},
    note = {Accepted}
    }
    

  9. Data Modeling with the Elliptical Gamma Distribution 🍒
          Suvrit Sra, Reshad Hosseini, Lucas Theis, Matthias Bethge
          Artificial Intelligence and Statistics (AISTATS 2015)
         
    @InProceedings{hoSra15,
    author = {Reshad Hosseini and Suvrit Sra and L. Theis and M. Bethge},
    title = {Statistical inference with the Elliptical Gamma Distribution},
    booktitle = {Artificial Intelligence and Statistics (AISTATS)},
    year = {2015},
    volume = 18,
    }
    


  10. Riemannian sparse coding for positive definite matrices 🍒
          Anoop Cherian, Suvrit Sra
          European Conference on Computer Vision (ECCV)
         
    @inproceedings{chSra14,
      title={Riemannian sparse coding for positive definite matrices},
      author={Anoop Cherian and Suvrit Sra},
      booktitle={ECCV 2014},
      pages={299--314},
      year={2014},
      publisher={Springer}
    }
    

  11. Geometric optimisation on positive definite matrices with application to elliptically contoured distributions 🍒
          Suvrit Sra and Reshad Hosseini
          Advances in Neural Information Processing Systems (NIPS)
         
    @InProceedings{sraHo13,
      author =       {Suvrit Sra and Reshad Hosseini},
      title =        {{Geometric optimisation on positive definite matrices with application to elliptically contoured distributions}},
      booktitle =    {Advances in Neural Information Processing Systems (NIPS)},
      year =         2013,
      month =        dec,
    }
    

  12. Jensen-Bregman LogDet Divergence for Efficient Similarity Computations on Positive Definite Tensors🍒
          Anoop Cherian, Suvrit Sra, Arindam Banerjee, and Nikos Papanikolopoulos
          IEEE Tran. Pattern. Analy. Mach. Intell. (TPAMI) Dec. 2012;
         
    @Article{chSra.pami,
      author =       {Anoop Cherian and Suvrit Sra and Arindam Banerjee and Nikolaos Papanikolopoulos},
      title =        {{Jensen-Bregman LogDet Divergence with Application to Efficient Similarity  Search for Covariance Matrices}},
      journal =      {IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI)},
      year =         2012,
      month =        {Dec.},
      note =         {14 pages},
    }
    

  13. A new metric on the manifold of kernel matrices with application to matrix geometric means 🍒🍀
          Suvrit Sra
          Advances of Neural Information Processing Systems (NIPS) 2012;
         
    @inproceedings{sra12.nips,
      title={A new metric on the manifold of kernel matrices with application to matrix geometric means},
      author={Suvrit Sra},
      booktitle={Advances in Neural Information Processing Systems},
      pages={144--152},
      year={2012}
    }
    

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