Conference Program


 (Add to Calendar)  Monday, August 20, 17:00 – 17:50 h, H0104:

Katya Scheinberg: Using randomized models in black-box and derivative free optimization

Chair: Luís Nunes Vicente



All derivative free methods rely on sampling the objective function at one or more points at each iteration. Direct search methods (developed by Dennis, Torczon, Audet, Vicente and others) rely on sample sets of defined configuration, but different scales. Model-based DFO methods (developed by Powell, Conn, Scheinberg, Toint, Vicente, Wild and others) rely on building interpolation models using sample points in proximity of the current best iterate. Constructing and maintaining these sample sets has been one of the most essential issues in DFO. Many of the existing results have been summarized in a book by Conn, Scheinberg, Vicente, where all the sampling techniques considered for deterministic functions are deterministic ones. We will discuss the new developments for using randomized sampled sets within the DFO framework. Randomized sample sets have many advantages over the deterministic sets. In particular, it is often easier to enforce "good" properties of the models with high probability, rather than the in the worst case. In addition, randomized sample sets can help automatically discover a good local low dimensional approximation to the high dimensional objective function. We will demonstrate how compressed sensing results can be used to show that reduced size random sample sets can provide full second order information under the assumption of the sparsity of the Hessian. We will discuss new convergence theory developed for the randomized models where we can, for instance, show that as long as the models are "good" with probability more than 1/2 then our trust region framework is globally convergent with probability 1 under standard assumptions.


Biographical sketch:

Katya Scheinberg is an associate professor in the Industrial and Systems Engineering Department at Lehigh University. A native from Moscow, she earned her undergraduate degree in operations research from the Lomonosov Moscow State University in 1992 and then received her Ph.D. in operations research from Columbia in 1997. Scheinberg was a Research Staff Member at the IBM T.J. Watson Research center for over a decade, where she worked on various applied and theoretical problems in optimization, until moving back to Columbia as a visiting professor in 2009 and later on to Lehigh. Her main research areas are related to developing practical algorithms (and their theoretical analysis) for various problems in continuous optimization, such as convex optimization, derivative free optimization, machine learning, quadratic programming, etc. Scheinberg has also published a book in 2008 titled, Introduction to Derivative Free Optimization, which is co-authored with Andrew R. Conn and Luis N. Vicente. She is currently the editor of Optima, the MOS newsletter, and an associate editor of SIOPT.

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