Improved KKT Complexity for First-Order Bilevel Optimization under Weak Lower-Level Convexity BB1XJ47PVW

URI	`m2://res/BB1XJ47PVW`
Kind	preprint
Creators	Jan Harold Alcantara, Masahiro Inoue, Akiko Takeda
Date	2026-09-30
MSC	49-XX, 90-XX, 93-XX
Subjects	arxiv math.OC
Scope	in

Expressions

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Stationarity estimate	statement	lemma 24	arxiv
Smoothing derivative estimates	statement	lemma 10	arxiv
Residual-based stopping rule for the Moreau evaluation	statement	lemma 19	arxiv
ENNAMCQ for few-shot learning	statement	proposition 16	arxiv
Stationarity properties of the Moreau gap	statement	proposition 12	arxiv
Polynomial smoothing estimates	statement	lemma 27	arxiv
Errors from an inexact Moreau evaluation	statement	lemma 11	arxiv
Overall first-order complexity	statement	corollary 7	arxiv
Uniform ENNAMCQ margin	statement	lemma 21	arxiv
Degeneracy of the exact Moreau-gap constraint	statement	proposition 14	arxiv
Stationarity bound at a penalty update	statement	lemma 22	arxiv
Well-definedness and descent	statement	lemma 4	arxiv
Deterioration of the ENNAMCQ margin	example	example 23	arxiv
ENNAMCQ for sample-reweighting models	statement	proposition 17	arxiv
ENNAMCQ	definition	definition 3	arxiv
Moreau envelope regularity	statement	proposition 8	arxiv
Approximate KKT point	definition	definition 2	arxiv
Complexity of the residual stopping rule	statement	lemma 20	arxiv
Finite penalty stabilization	statement	lemma 5	arxiv
Interpretation of approximate feasibility	statement	corollary 13	arxiv
KKT estimates at a non-update iteration	statement	lemma 26	arxiv
ENNAMCQ for sigmoid-reweighted classification	statement	corollary 18	arxiv
Feasibility and complementarity	statement	lemma 25	arxiv
Automatic ENNAMCQ without nonconstant affine segments	statement	proposition 15	arxiv
Outer-iteration complexity	statement	theorem 6	arxiv
Z9A4AQ7TJ8	statement	lemma 9	arxiv