6 papers
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…
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 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 for multioperator comonotone inclusions with applications to multiblock optimization
Jan Harold Alcantara, Minh N. Dao, Akiko Takeda
We study the convergence of the adaptive Douglas--Rachford (aDR) algorithm for solving a multioperator inclusion problem involving the sum of maximally comonotone operators. To add…
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…
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…