arXiv subjects

Hidenori Iwakiri

Publications and source records attributed to Hidenori Iwakiri.

2 recordsLinked to original sources

arXiv2024

Prediction-Correction Algorithm for Time-Varying Smooth Non-Convex Optimization

Time-varying optimization problems are prevalent in various engineering fields, and the ability to solve them accurately in real-time is becoming increasingly important. The prediction-correction algorithms used in smooth time-varying optimization can achieve better accuracy than that of the time-varying gradient descent (TVGD) algorithm. However, none of the existing prediction-correction algorithms can be applied to general non-strongly-convex functions, and most of them are not computationally efficient enough to solve large-scale problems. Here, we propose a new prediction-correction algorithm that is applicable to large-scale and general non-convex problems and that is more accurate than TVGD. Furthermore, we present convergence analyses of the TVGD and proposed prediction-correction algorithms for non-strongly-convex functions for the first time. In numerical experiments using synthetic and real datasets, the proposed algorithm is shown to be able to reduce the convergence error as the theoretical analyses suggest and outperform the existing algorithms.

math.OC↗

arXiv2022

Single Loop Gaussian Homotopy Method for Non-convex Optimization

The Gaussian homotopy (GH) method is a popular approach to finding better stationary points for non-convex optimization problems by gradually reducing a parameter value $t$, which changes the problem to be solved from an almost convex one to the original target one. Existing GH-based methods repeatedly call an iterative optimization solver to find a stationary point every time $t$ is updated, which incurs high computational costs. We propose a novel single loop framework for GH methods (SLGH) that updates the parameter $t$ and the optimization decision variables at the same. Computational complexity analysis is performed on the SLGH algorithm under various situations: either a gradient or gradient-free oracle of a GH function can be obtained for both deterministic and stochastic settings. The convergence rate of SLGH with a tuned hyperparameter becomes consistent with the convergence rate of gradient descent, even though the problem to be solved is gradually changed due to $t$. In numerical experiments, our SLGH algorithms show faster convergence than an existing double loop GH method while outperforming gradient descent-based methods in terms of finding a better solution.

math.OC↗