Dai–Liao-type Riemannian optimization for solving the Gough–Stewart platform

Abstract

We introduce a class of Dai–Liao-type Riemannian conjugate gradient (CG) methods that achieve global convergence without relying on the Gauss lemma, typically invoked under strong convexity assumptions. The proposed search directions are proven to satisfy a sufficient descent property independently of the traditional Riemannian line search conditions. Furthermore, we design an adaptive min(max) strategy, inspired by trust-region techniques, to regulate the search process through bounded parameters ${\mu }_{min}$ and ${\mu }_{max}$, ensuring numerical stability. A notable feature of our convergence analysis is that it avoids the standard practice of reducing the CG parameter ${\beta }_{k+1}$ to a fixed form, offering a more flexible theoretical framework.