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Center for Nonlinear Studies |
Direct Sparse factorization techniques have significantly advanced over the last two decades and have become an indispensible tool of every large-scale optimization algorithm. From standardinterior point methods for solving LPs and NLPs to state-of-the-art stochastic optimization algorithms, direct sparse methods provide thenecessary ingredient for efficient and accurate parallel computation of indefinite LDLT factorizations, Schur complement computation,and on-the-fly calculation of selected entries of the inverse. We will discuss the details of algorithmic implementations of theaforementioned sparse kernels inside the parallel direct sparse solver PARDISO, along with the underlying fill-in reducing ordering techniquesessential for low memory implementations and increased parallelism. We will then proceed to structure exploiting data compression sparsetechniques that significantly accelerate the solution of different types of optimal power flow problems, commonly solved by transmissionsystem operators for the economic and secure dispatch of electricity generation. Examples involve multiperiod optimal power flow problemsincluding storage devices ranging up to KKT systems with 108 rows and security constrained optimal power flow problems on several networks of increased complexity.
Host: Russell Bent