Related papers: Forward-backward-forward dynamics for bilevel equi…
In this paper we present the bilevel equilibrium problem under conditions of pseudomonotonicity. Using Bregman distances on Hadamard manifolds we propose a framework for to analyse the convergence of a proximal point algorithm to solve this…
We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including H\"olderian growth…
The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…
In this article, we study two methods for solving monotone inclusions in real Hilbert spaces involving the sum of a maximally monotone operator, a monotone-Lipschitzian operator, a cocoercive operator, and a normal cone to a vector…
We propose a Forward-Backward Truncated-Newton method (FBTN) for minimizing the sum of two convex functions, one of which smooth. Unlike other proximal Newton methods, our approach does not involve the employment of variable metrics, but is…
Generalizable manipulation requires that robots be able to interact with novel objects and environment. This requirement makes manipulation extremely challenging as a robot has to reason about complex frictional interaction with uncertainty…
A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…
In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and…
We present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier…
In safety-critical control, managing safety constraints with high relative degrees and uncertain obstacle dynamics pose significant challenges in guaranteeing safety performance. Robust Control Barrier Functions (RCBFs) offer a potential…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…
In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection-algorithm,…
In this paper, we introduce a large class of convergent numerical methods, based on (linear) basis function regression technique, to approximate the solution to a forward-backward stochastic differential equation with jumps (FBSDEJ…
We formulate and solve the fixed horizon linear quadratic covariance steering problem in continuous time with a terminal cost measured in Hilbert-Schmidt (i.e., Frobenius) norm error between the desired and the controlled terminal…
In this paper, we exploit the so-called value function reformulation of the bilevel optimization problem to develop duality results for the problem. Our approach builds on Fenchel-Lagrange-type duality to establish suitable results for the…
We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…
We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the…
We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…