Linearly constrained bilevel optimization: A smoothed implicit gradient approach

P Khanduri, I Tsaknakis, Y Zhang… - International …, 2023 - proceedings.mlr.press
This work develops analysis and algorithms for solving a class of bilevel optimization
problems where the lower-level (LL) problems have linear constraints. Most of the existing …

Rate-improved inexact augmented Lagrangian method for constrained nonconvex optimization

Z Li, PY Chen, S Liu, S Lu, Y Xu - … Conference on Artificial …, 2021 - proceedings.mlr.press
First-order methods have been studied for nonlinear constrained optimization within the
framework of the augmented Lagrangian method (ALM) or penalty method. We propose an …

Efficiently esca** saddle points in bilevel optimization

M Huang, X Chen, K Ji, S Ma, L Lai - ar** strict saddle points of the Moreau envelope in nonsmooth optimization
D Davis, M Díaz, D Drusvyatskiy - SIAM Journal on Optimization, 2022 - SIAM
Recent work has shown that stochastically perturbed gradient methods can efficiently
escape strict saddle points of smooth functions. We extend this body of work to nonsmooth …

A Newton-CG based barrier method for finding a second-order stationary point of nonconvex conic optimization with complexity guarantees

C He, Z Lu - SIAM Journal on Optimization, 2023 - SIAM
In this paper we consider finding an approximate second-order stationary point (SOSP) of
nonconvex conic optimization that minimizes a twice differentiable function over the …