Scalable libraries for solving systems of nonlinear equations and unconstrained minimization problems

Developing portable and scalable software for the solution of large-scale optimization problems presents many challenges that traditional libraries do not adequately meet. Using object-oriented design in conjunction with other innovative techniques, we address these issues within the SNES (Scalable Nonlinear Equation Solvers) and SUMS (Scalable Unconstrained Minimization Solvers) packages, which are part of the multilevel PETSc (Portable, Extensible Tools for Scientific computation) library. The paper focuses on our design philosophy and its benefits in providing a uniform and versatile framework for developing optimization software and solving large-scale nonlinear problems. We also consider a three-dimensional anisotropic Ginzburg-Landau model as a representative application that exploits the packages' flexible interface with user specified data structures and customized routines for function evaluation and preconditioning.<
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