11 papers · 1 filter
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…
A relaxed version of Ryu's three-operator splitting method for structured nonconvex optimization
Jan Harold Alcantara, Felipe Atenas
In this work, we propose a modification of Ryu's splitting algorithm for minimizing the sum of three functions, where two of them are convex with Lipschitz continuous gradients, an…
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…
Accelerated projected gradient algorithms for sparsity constrained optimization problems
Jan Harold Alcantara, Ching-pei Lee
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an -norm constraint. Throu…
Global convergence and acceleration of projection methods for feasibility problems involving union convex sets
Jan Harold Alcantara, Ching-pei Lee
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number…
Unified Smoothing Approach for Best Hyperparameter Selection Problem Using a Bilevel Optimization Strategy
Jan Harold Alcantara, Chieu Thanh Nguyen, Takayuki Okuno +2
Strongly motivated from use in various fields including machine learning, the methodology of sparse optimization has been developed intensively so far. Especially, the recent advan…
Method of Alternating Projection for the Absolute Value Equation
Jan Harold Alcantara, Jein-Shan Chen, Matthew K. Tam
A novel approach for solving the general absolute value equation where and is presented. We reformulate the equati…