Qiankun Shi

We study oracle-complexity lower bounds for first-order methods applied to smooth equality-constrained nonconvex optimization, separating two components of approximate KKT accuracy: feasibility and stationarity. Under iteration-wise Jacobian regularity, we prove a lower bound of order \(\Omega(\frac{L_c\Delta_c}{\sigma^2}+\log\log(\frac{\sigma^2}{L_c\epsilon}))\) to achieve \(\epsilon\)-feasibility. For stationarity, we construct a nonlinear equality-constrained hard instance whose multiplier-minimized stationarity residual reduces exactly to … Read more

In this paper, we study nonconvex equality-constrained optimization problems in which only stochastic first-order approximations of the objective and constraint functions are available. Owing to the stochasticity in both objective and constraints, most existing stochastic first-order methods incur relatively high oracle complexity, particularly in terms of stochastic constraint function evaluations. To address this issue, we … Read more

In this paper, we study a penalty method for stochastic equality-constrained optimization, where both the objective and constraints are expressed in general expectation form. We introduce a novel adaptive strategy for updating the penalty parameter, guided by iteration progress to balance reductions in the penalty function with improvements in constraint violation, while each penalty subproblem … Read more