Title: A Generalized Inexact SQP Framework for Large-Scale Optimization Speaker: Denis Ridzal, von Neumann Fellowship Candidate, Rice University Date/Time: Monday, January 30, 2006, 10:00 – 11:00 amLocation: Building 980, Room 95 (Sandia NM) Building 915, Room S145 (Sandia CA) Brief Abstract: Sequential quadratic programming (SQP) methods have been used successfully for the solution of large-scale constrained nonlinear optimization problems. This talk focuses on the design of a class of general-purpose SQP algorithms that allow for an efficient integration of inexact linear system solvers. Each iteration within an SQP method requires the solution of several linear systems, whose system matrix/operator involves the linearized constraints. Most existing implementations of SQP algorithms use direct linear algebra methods to solve these systems. For many applications in science and engineering this is infeasible, because the systems are too large or the matrices associated with the linearized constraints are not formed explicitly. Instead, iterative solvers, such as preconditioned Krylov subspace methods, have to be applied for the approximate solution of the linear systems arising within the SQP algorithm.I present an algorithmic framework in which the optimization algorithm dynamically adjusts the stopping tolerances for all iterative linear system solves. The stopping tolerances are based on the progress of the optimization algorithm, can be easily computed, and are sufficient to guarantee first--order global convergence of the algorithm. The framework also allows for a rigorous integration of domain-decomposition preconditioners for so-called KKT systems, which are discussed in the second part of the talk. CSRI POC: Bill Hart, (505) 844-2217 |