Related papers: Homotopy methods for higher order shape optimizati…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
The problem of covering a region of the plane with a fixed number of minimum-radius identical balls is studied in the present work. An explicit construction of bi-Lipschitz mappings is provided to model small perturbations of the union of…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
We present a numerical method to efficiently solve optimization problems governed by large-scale nonlinear systems of equations, including discretized partial differential equations, using projection-based reduced-order models accelerated…
For real-time multirotor kinodynamic motion planning, the efficiency of sampling-based methods is usually hindered by difficult-to-sample homotopy classes like narrow passages. In this paper, we address this issue by a hybrid scheme. We…
Automating design minimizes errors, accelerates the design process, and reduces cost. However, automating robot design is challenging due to recursive constraints, multiple design objectives, and cross-domain design complexity possibly…
We propose an automatic algorithm for 3D inverse electromagnetic scattering based on the combination of topological derivatives and regularized Gauss-Newton iterations. The algorithm is adapted to decoding digital holograms. A hologram is a…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for finite plasticity within a logarithmic strain framework. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement…
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…
Second-order methods for neural network optimization have several advantages over methods based on first-order gradient descent, including better scaling to large mini-batch sizes and fewer updates needed for convergence. But they are…
We study a multi-objective scheduling problem on two dedicated processors. The aim is to minimize simultaneously the makespan, the total tardiness and the total completion time. This NP-hard problem requires the use of well-adapted methods.…
Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…
In this paper, we consider an unconstrained stochastic optimization problem where the objective function exhibits high-order smoothness. Specifically, we propose a new stochastic first-order method (SFOM) with multi-extrapolated momentum,…
The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then…
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…