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The advent of efficient interior point optimization methods has enabled thetractable solution of large-scale linear and nonlinear programming (NLP)problems. A prominent example of such a method is seen in Ipopt, a widely-used,open-source nonlinear optimization solver. Algorithmically, Ipopt depends onthe use of a sparse symmetric indefinite linear system solver, which is heavilyemployed within the optimization of barrier subproblems. As such, theperformance and reliability of Ipopt is dependent on the properties of theselected linear solver. Inspired by a trend in mathematical programming towardsolving larger and more challenging NLPs, this work explores two corequestions: first, how does the scalability of available linear solvers, many ofwhich exhibit shared-memory parallelism, impact Ipopt performance; and second,does the best linear solver vary across NLP problem classes, includingnonlinear network problems and problems constrained by partial differentialequations? To better understand these properties, this paper first describesavailable open- and closed-source, serial and parallel linear solvers and thefundamental differences among them. Second, it introduces the coupling of a newopen-source linear solver capable of heterogeneous parallelism over multi-corecentral processing units and graphics processing units. Third, it compareslinear solvers using a variety of mathematical programming problems, includingstandard test problems for linear and nonlinear optimization, optimal powerflow benchmarks, and scalable two- and three-dimensional partial differentialequation and optimal control problems. Finally, linear solver recommendationsare provided to maximize Ipopt performance across different applicationdomains.

Exploring Benefits of Linear Solver Parallelism on Modern Nonlinear Optimization Applications