Optimization

What if the hardest part of finance isn’t prediction, but precision? Behind every real-time portfolio adjustment or split-second options quote lies a giant math problem: solving Ax = b, where A is large, sparse, and often very poorly behaved. In traditional finance pipelines, iterative solvers like GMRES or its flexible cousin FGMRES are tasked with solving these linear systems — be it from a Markowitz portfolio optimization or a discretized Black–Scholes PDE for option pricing. But when the matrix A is ill-conditioned (which it often is), convergence slows to a crawl. Preconditioning helps, but tuning these parameters is more art than science — until now. ...

Traditionally, solving optimization problems involves meticulous human effort: crafting mathematical models, selecting appropriate algorithms, and painstakingly tuning hyperparameters. Despite the rigor, these human-centric processes are prone to bottlenecks, limiting the industrial adoption of cutting-edge optimization techniques. Wenhao Li and colleagues 1 challenge this paradigm in their recent paper, proposing an innovative shift toward evolutionary agentic workflows, powered by foundation models (FMs) and evolutionary algorithms. Understanding the Optimization Space Optimization problems typically traverse four interconnected spaces: ...