Related papers: Linearizations and optimization problems in diffeo…
We introduce a geometric and operator-theoretic formalism viewing optimization algorithms as discrete connections on a space of update operators. Each iterative method is encoded by two coupled channels-drift and diffusion-whose algebraic…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
General multi-objective optimization problems are often solved by a sequence of parametric single objective problems, so-called scalarizations. If the set of nondominated points is finite, and if an appropriate scalarization is employed,…
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…
This paper deals with some basic constructions of linear and multilinear algebra on finite-dimensional diffeological vector spaces. We consider the diffeological dual formally checking that the assignment to each space of its dual defines a…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
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;…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
Gradient-based methods successfully train highly overparameterized models in practice, even though the associated optimization problems are markedly nonconvex. Understanding the mechanisms that make such methods effective has become a…
An iterative Finite Element method predicated on a linearisation of the weak form around a reference configuration is derived for general, three-dimensional, free-surface flows, including systems with moving contact lines. The method is a…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…