Related papers: Preconditioned Nonlinear Conjugate Gradient Method…
An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…
Interior point methods are widely used for different types of mathematical optimization problems. Many implementations of interior point methods in use today rely on direct linear solvers to solve systems of equations in each iteration. The…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
We propose a GPU-based iterative method for accelerated elastodynamic simulation with the log-barrier-based contact model. While Newton's method is a conventional choice for solving the interior-point system, the presence of ill-conditioned…
We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. Our method is based on a non-smooth Newton iteration that solves the underlying nonlinear complementarity problems (NCPs)…
Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but…
In this article, we propose an algorithm for the nonlinear conjugate gradient method to find a Pareto critical point of unconstrained multiobjective interval optimization problems. In this algorithm, we use the Wolfe line search procedure…
Nonlinear conjugate gradients are among the most popular techniques for solving continuous optimization problems. Although these schemes have long been studied from a global convergence standpoint, their worst-case complexity properties…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…
We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients $A$. We assume that the preconditioner is SPD on each step, and…
We present a GPU-friendly framework for real-time implicit simulation of elastic material in the presence of frictional contacts. The integration of hyperelasticity, non-interpenetration contact, and friction in real-time simulations…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
In parallel simulation, convergence and parallelism are often seen as inherently conflicting objectives. Improved parallelism typically entails lighter local computation and weaker coupling, which unavoidably slow the global convergence.…
The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
Off-lattice agent-based models (or cell-based models) of multicellular systems are increasingly used to create in-silico models of in-vitro and in-vivo experimental setups of cells and tissues, such as cancer spheroids, neural crest cell…
In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…
High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often…