2022/05/17 by Raphael Chinchilla, Chinchilla, Raphael, Guosong Yang +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2205.08038
openalex publication_date 2022/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the problem of finding a local solution to a nonconvex-nonconcave minmax optimization using Newton type methods, including interior-point ones. We modify the Hessian matrix of these methods such that, at each step, the modified Newton update direction can be seen as the solution to a quadratic program that locally approximates the minmax problem. Moreover, we show that by selecting the modification in an appropriate way, the only stable equilibrium points of the algorithm's iterations are local minmax points. As a consequence, the algorithm can only converge towards an equilibrium point if such point is a local minmax, and it will escape if the point is not a local minmax. Using numerical examples, we show that the computation time of our algorithm scales roughly linearly with the number of nonzero elements in the Hessian.