• Summary: The focus of this work is simulation-based optimization using data fit and hierarchical surrogates. For computational intensive simulations, the use of surrogates can help reduce the overall cost of optimization. Global convergence is guaranteed with the use of a trust region and when consistency between the surrogate and simulation model is enforced for each iterate. For infeasible starting points, a heuristic homotopy approach is used to balance progress towards feasibility and optimality, further reducing overall computational costs. Work on multigrid optimization as a special case of hierarchical surrogate optimization is planned.
• Collaborators: Mike Eldred (Sandia)
• Publications/Presentations:
  • "Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, and Reduced-Order Models." Michael S. Eldred and Daniel M Dunlavy. AIAA-2006-7117, Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, September 2006.  [Abstract]  [PDF]

• Summary: The goal of this work has been to produce an global optimization algorithm for finding a global minimizer for potential energy functions for pairs of homologous, or sequentially related, proteins. The method developed, Homotopy Optimization using Perturbations and Ensembles (HOPE), shares features with comparative modeling, smoothing methods, and simulated annealing, all of which have been used by various researchers in the past to solve to predict the native state of proteins, or simplified models of proteins and clusters of atoms. The extension of HOPE as a general global optimization algorithm appears promising and further work in the area of constrained optimization is planned.
• Collaborators: Dianne P. O'Leary (Maryland)
• Publications:
  • "Homotopy Optimization Methods for Global Optimization." Daniel M. Dunlavy and Dianne P. O'Leary. Sandia National Laboratories Technical Report, SAND2005-7495, December 2005.  [Abstract]  [PDF]
  • "HOPE: A Homotopy Optimization Method for Protein Structure Prediction." Daniel M. Dunlavy, Dianne P. O'Leary, Dmitri Klimov and D. Thirumalai. Journal of Computational Biology, 12(10):1275-1288, December 2005.  [Abstract]  [PDF]
  • "Homotopy Optimization Methods and Protein Structure Prediction." Daniel M. Dunlavy. Ph.D. Dissertation, AMSC Program, University of Maryland, August 2005.  [Abstract]  [Request]

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• Summary: Implementation and testing of algorithms for solving structured eigenvalue problems using perplectic orthogonal (i.e., centrosymmetric orthogonal) transformations. These algorithms are Jacobi-like iterative methods for solving the complete eigenvalue problem for matrices with the double structure of symmetry/skew-symmetry across both the diagonal as well as anti-diagonal. Based on the direct solution of 4-by-4 subproblems constructed via quaternions, the algorithms calculate structured orthogonal bases for the invariant subspaces of the associated matrix. In addition to preserving structure, these methods are inherently parallelizable, numerically stable, and show asymptotic quadratic convergence.
• Collaborators: Nil Mackey (W. Michigan), D. Steven Mackey (W. Michigan)
• Publications:
  • "Structure Preserving Algorithms for Perplectic Eigenproblems." D. Steven Mackey, Niloufer Mackey, and Daniel M. Dunlavy. Electronic Journal of Linear Algebra, 13:10-39, February 2005.  [Abstract]  [PDF]

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• Summary: Development and application of linear and multilinear algebra techniques for analysis of information, with an emphasis on textual data. The focus to date has been on information retrieval, document clustering by topic, automatic text summarization, and multiple-link data analysis techniques as well as on the development of a modular hybrid system for data analysis (QCS).
• Collaborators: Tammy Kolda (Sandia), Philip Kegelmeyer (Sandia), Dianne P. O'Leary (Maryland), John M. Conroy (Center for Computing Sciences), Judith D. Schlesinger (Center for Computing Sciences)
• Publications:
  • "QCS: A System for Querying, Clustering and Summarizing Documents." Daniel M. Dunlavy, Dianne P. O'Leary, John M. Conroy, and Judith D. Schlesinger. Information Processing & Management, in press (accepted October 2006).  [Abstract]  [Preprint PDF]
  • "Multilinear Algebra for Analyzing Data with Multiple Linkages." Daniel M. Dunlavy, Tamara G. Kolda, and W. Philip Kegelmeyer. Sandia National Laboratories Technical Report, SAND2006-2079, April 2006.  [Abstract]  [PDF]
  • "QCS: An Information Retrieval System for Improving Efficiency in Scientific Literature Searches." Daniel M. Dunlavy. M.S. Scholarly Paper, Applied Mathematics and Scientific Computation Program, University of Maryland, December 2003.  [Abstract]  [PDF]
  • "From TREC to DUC to TREC Again." John M. Conroy, Dianne P. O'Leary, and Daniel M. Dunlavy. Proceedings of the Twelfth Text Retrieval Conference (TREC), November 2003.  [Abstract]  [PDF]
  • "Performance of a Three-Stage System for Multi-Document Summarization." Daniel M. Dunlavy, John M. Conroy, Judith D. Schlesinger, Sarah A. Goodman, Mary Ellen Okurowski, Dianne P. O'Leary, and Han van Halteren. Proceedings of the Document Understanding Conference (DUC), June 2003.  [Abstract]  [PS]
  • "QCS: A Tool for Querying, Clustering, and Summarizing Documents." Daniel M. Dunlavy, John M. Conroy and Dianne P. O'Leary. Proceedings of the HLT-NAACL Conference, June 2003.  [Abstract]  [PDF]

• Summary: The goal of this work has been to produce an global optimization algorithm for finding a global minimizer for potential energy functions for pairs of homologous, or sequentially related, proteins. The method developed, Homotopy Optimization using Perturbations and Ensembles (HOPE), shares features with comparative modeling, smoothing methods, and simulated annealing, all of which have been used by various researchers in the past to solve to predict the native state of proteins, or simplified models of proteins and clusters of atoms.
• Collaborators: Dianne P. O'Leary (Maryland), D. Thirumalai (Maryland), Dmitri Klimov (George Mason)
• Publications:
  • "HOPE: A Homotopy Optimization Method for Protein Structure Prediction." Daniel M. Dunlavy, Dianne P. O'Leary, Dmitri Klimov and D. Thirumalai. Journal of Computational Biology, 12(10):1275-1288, December 2005.  [Abstract]  [PDF]
  • "Homotopy Optimization Methods and Protein Structure Prediction." Daniel M. Dunlavy. Ph.D. Dissertation, AMSC Program, University of Maryland, August 2005.  [Abstract]  [Request]

• Summary: In this work, we solve for the steady­state solution of non­linear DAE's arising from circuit design using finite­difference and harmonic­balancing methods. Various numerical differentiation techniques are considered. Small problems are solved using direct methods while systems of larger size are solved using iterative methods. We apply various preconditioners to speed up the convergence and compare their effectiveness by looking at the number of iterations needed for the iterative method to converge.
• Collaborators: Sookhyung Joo, Runchang Lin, Roummel Marcia, Aurelia Minut, Jianzhong Sun, Robert Melville (as part of an IMA Workshop)
• Publications:
  • "Numerical Steady-State Solutions of Non-Linear DAE's Arising in RF Communication Circuit Design." Danny Dunlavy, Sookhyung Joo, Runchang Lin, Roummel Marcia, Aurelia Minut, and Jianzhong Sun (Robert Melville, mentor). IMA Preprint Series 1752-1, February 2001.  [Abstract]  [PDF]

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