Related papers: Forward-backward-forward dynamics for bilevel equi…
The double pendulum, a simple system of classical mechanics, is widely studied as an example of, and testbed for, chaotic dynamics. In 2016, Maiti et al. studied a generalization of the simple double pendulum with equal point-masses at…
In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…
In this paper, we propose two projection dynamical systems for solving inverse quasi-variational inequality problems in finite-dimensional Hilbert spaces-one ensuring finite-time stability and the other guaranteeing fixed-time stability. We…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…
In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in…
Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new Domain Decomposition Scheme to solve forward-backward stochastic differential equations (FBSDEs) parallely. We…
This is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T.…
We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level…
Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…
This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…
We propose a third order dynamical system for solving a nonlinear equation in Hilbert spaces where the operator is cocoercive with respect to the solutions set. Under mild conditions on the parameters, we establish the existence and…
The backpropagation algorithm, or backprop, is a widely utilized optimization technique in deep learning. While there's growing evidence suggesting that models trained with backprop can accurately explain neuronal data, no backprop-like…
This paper presents a new geometric and recursive algorithm for analytically computing the forward dynamics of heavy-duty parallel-serial mechanisms. Our solution relies on expressing the dynamics of a class of linearly-actuated parallel…
This paper studies the fundamental properties of the high-order forward-backward splitting mapping (HiFBS) and its associated forward-backward envelope (HiFBE) through the lens of high-order regularization for nonconvex composite functions.…
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can…
The covariant light-front equations have been solved exactly for a two fermion system with different boson exchange ladder kernels. We present a method to study the cutoff dependence of these equations and to determine whether they need to…
The light-front dynamics (LFD) of the scalar field model theory is analyzed to solve the two-body bound-state problem. The light-front two-body bound-state equation is extended to the full LFD kernel including the ladder, cross-ladder,…