6 papers · 1 filter
Computing Kurdyka-Łojasiewicz exponents via composition and symmetry
Cédric Josz, Wenqing Ouyang
We devise calculus rules for the Kurdyka-Łojasiewicz exponent using the rank theorem and Lie group actions. They apply to a wide class of composite and invariant functions, and are…
A linesearch-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimization
Hanfeng Zeng, Wenqing Ouyang, Andre Milzarek
We propose a novel linesearch variant of the trust region normal map-based semismooth Newton method developed in [Ouyang and Milzarek, Math. Program. 212(1-2), 389--435 (2025)] for…
A MINRES-based Linesearch Algorithm for Nonconvex Optimization with Non-positive Curvature Detection
Hanfeng Zeng, Yang Liu, Wenqing Ouyang +1
We propose a MINRES-based Newton-type algorithm for solving unconstrained nonconvex optimization problems. Our approach uses the minimal residual method (MINRES), a well-known solv…
Reachability of gradient descent
Cédric Josz, Wenqing Ouyang
We show that gradient descent can converge to any local minimum of a smooth semi-algebraic function. This holds if the step sizes are nonsummable and sufficiently small. The same r…
Kurdyka-Łojasiewicz exponent via square transformation
Wenqing Ouyang
We consider one of the most common reparameterization techniques, the square transformation. Assuming the original objective function is the sum of a smooth function and a polyhedr…
Anderson Acceleration for Nonconvex ADMM Based on Douglas-Rachford Splitting
Wenqing Ouyang, Yue Peng, Yuxin Yao +2
The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly t…