Related papers: An Approximate Newton Smoothing Method for Shape O…
Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…
We propose a multidimensional smoothing spline algorithm in the context of manifold learning. We generalize the bending energy penalty of thin-plate splines to a quadratic form on the Sobolev space of a flat manifold, based on the Frobenius…
The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel…
Machine learning has opened new frontiers in purely data-driven algorithms for data assimilation in, and for forecasting of, dynamical systems; the resulting methods are showing some promise. However, in contrast to model-driven algorithms,…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that only stochastic information of the gradients of the objective function is available via a stochastic first-order oracle…
Quasi-Newton methods form an important class of methods for solving nonlinear optimization problems. In such methods, first order information is used to approximate the second derivative. The aim is to mimic the fast convergence that can be…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape…
Operator learning is a recent development in the simulation of Partial Differential Equations (PDEs) by means of neural networks. The idea behind this approach is to learn the behavior of an operator, such that the resulting neural network…
A general method for estimating the approximation numbers of composition operators on $\Ht$, using finite-dimensional model subspaces, is studied and applied in the case when the symbol of the operator maps the unit disc to a domain whose…
We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…
We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting…
This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber…
In this paper we propose a stable and robust strategy to approximate the 3d incompressible hydrostatic Euler and Navier-Stokes systems with free surface. Compared to shallow water approximation of the Navier-Stokes system, the idea is to…
This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…
In this paper we introduce an abstract nonsmooth optimization problem and prove existence and uniqueness of its solution. We present a numerical scheme to approximate this solution. The theory is later applied to a sample static contact…
We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is…
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…
We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…