Related papers: Constraint interface preconditioning for topology …

We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…

Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a…

Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline…

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 this article we construct and analyze multigrid preconditioners for discretizations of operators of the form D+K* K, where D is the multiplication with a relatively smooth positive function and K is a compact linear operator. These…

Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…

The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…

We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…

In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…

This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…

In this paper, we proposed an interior point method for constrained optimization, which is characterized by the using of quasi-tangential subproblem. This algorithm follows the main ideas of primal dual interior point methods and…

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…

In the past decade, a combination of unfitted finite elements (or XFEM) with the Nitsche method has become a popular discretization method for elliptic interface problems. This development started with the introduction and analysis of this…

In this paper we propose two variants of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the new preconditioners, we use the simplest coarse solver…

In this work we consider topology optimization of systems, which are governed by the external Bernoulli free boundary problem. We utilize the so-called pseudo-solid approach to solve the governing free boundary problems during the…