Mathtt {Tenscalc}: a toolbox to generate fast code to solve nonlinear constrained minimizations and compute Nash equilibria

Abstract

We describe the toolbox mathtt {Tenscalc} that generates specialized C-code to solve nonlinear constrained optimizations and to compute Nash equilibria. mathtt {Tenscalc} is aimed at scenarios where one needs to solve very fast a large number of optimizations that are structurally similar. This is common in applications where the optimizations depend on measured data and one wants to compute optima for large or evolving datasets, e.g., in robust estimation and classification, maximum likelihood estimation, model predictive control (MPC), moving horizon estimation (MHE), and combined MPC-MHE (which requires the computation of a saddle-point equilibria). mathtt {Tenscalc} is mostly aimed at generating solvers for optimizations with up to a few thousands of optimization variables/constraints and solve times up to a few milliseconds. The speed achieved by the solver arises from a combination of features: reuse of intermediate computations across and within iterations of the solver, detection and exploitation of matrix sparsity, avoidance of run-time memory allocation and garbage collection, and reliance on flat code that improves the efficiency of the microprocessor pipelining and caching. All these features have been automated and embedded into the code generation process. We include a few representative examples to illustrate how the speed and memory footprint of the solver scale with the size of the problem.