6 papers
Improved KKT Complexity for First-Order Bilevel Optimization under Weak Lower-Level Convexity
Jan Harold Alcantara, Masahiro Inoue, Akiko Takeda
We study deterministic first-order bilevel optimization under weak lower-level convexity, allowing nonconvex lower-level objectives and without assuming strong convexity, the Polya…
A Splitting Framework for Composite Semimonotone Inclusions
Jan Harold Alcantara, Minh N. Dao, Akiko Takeda
We introduce a general framework for composite inclusion problems with affine constraints, covering both monotone and semimonotone regimes. The central idea is a new interpretation…
Douglas--Rachford for multioperator comonotone inclusions with applications to multiblock optimization
Jan Harold Alcantara, Minh N. Dao, Akiko Takeda
We study the doubly relaxed Douglas--Rachford (DR) algorithm for solving a multioperator inclusion problem involving the sum of maximally comonotone operators. To address such prob…
Douglas--Rachford algorithm for nonmonotone multioperator inclusion problems
Jan Harold Alcantara, Akiko Takeda
The Douglas--Rachford algorithm is a classic splitting method for finding a zero of the sum of two maximal monotone operators. It has also been applied to settings that involve one…
A four-operator splitting algorithm for nonconvex and nonsmooth optimization
Jan Harold Alcantara, Ching-pei Lee, Akiko Takeda
In this work, we address a class of nonconvex nonsmooth optimization problems where the objective function is the sum of two smooth functions (one of which is proximable) and two n…
Theoretical smoothing frameworks for nonsmooth simple bilevel problems
Jan Harold Alcantara, Akiko Takeda
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulat…