Related papers: Newton Algorithm on Constraint Manifolds and the 5…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency under high-accuracy requirements. To this end, we propose a…
Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…
A well-known combinatorial algorithm can decide generic rigidity in the plane by determining if the graph is of Pollaczek-Geiringer-Laman type. Methods from matroid theory have been used to prove other interesting results, again under the…
Near full-null degenerate singular points of analytic vector fields, asymptotic behaviors of orbits are not given by eigenvectors but totally decided by nonlinearities. Especially, in the case of high full-null degeneracy, i.e., the lowest…
We present a computational method for the simulation of the solidification of multicomponent alloys in the sharp-interface limit. Contrary to the case of binary alloys where a fixed point iteration is adequate, we hereby propose a…
This paper formulates an elementary algorithm for resolution of singularities in a neighborhood of a singular point over a field of characteristic zero. The algorithm is composed of finite sequences of Newton polyhedra and monomial…
Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated,…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…
This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplified by a lengthy list of examples from the literature,…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…
In probabilistic modeling, parameter estimation is commonly formulated as a minimization problem on a parameter manifold. Optimization in such spaces requires geometry-aware methods that respect the underlying information structure. While…
We present an algorithm for the following problem. Given a triangulated 3-manifold M and a (possibly non-simple) closed curve on the boundary of M, decide whether this curve is contractible in M. Our algorithm runs in space polynomial in…
This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple,…
This paper focuses on discussing Newton's method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the…
The presence of task constraints imposes a significant challenge to motion planning. Despite all recent advancements, existing algorithms are still computationally expensive for most planning problems. In this paper, we present Constrained…
Many problems in operations research require that constraints be specified in the model. Determining the right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and…
An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic projection, approximation by trigonometric polynomials, and…
In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological…