Related papers: Variational point-obstacle avoidance on Riemannian…

This note is devoted to continuity results of the time derivative of the solution to the one-dimensional parabolic obstacle problem with variable coefficients. It applies to the smooth fit principle in numerical analysis and in financial…

We study the variational problem for $N$-parallel curves on a Finslerian surface by means of Exterior Differential Systems using Griffiths' method. We obtain the conditions when these curves are extremals of a length functional and write…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

In this paper, we present an on-board vision-based approach for avoidance of moving obstacles in dynamic environments. Our approach relies on an efficient obstacle detection and tracking algorithm based on depth image pairs, which provides…

We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimization are often based on techniques from differential…

This paper introduces a new class of variational inequalities where the obstacle is placed in the exterior domain that is disjoint from the observation domain. This is carried out with the help of nonlocal fractional operators. The need for…

We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…

We consider the optimization problem with a generally quadratic matrix constraint of the form $X^TAX = J$, where $A$ is a given nonsingular, symmetric $n\times n$ matrix and $J$ is a given $k\times k$ symmetric matrix, with $k\leq n$,…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…

In these notes we study the Dirichlet problem for critical points of a convex functional of the form \[ F(u)=\int_{\Omega}\phi\left( \left\vert \nabla u\right\vert \right) , \] where $\Omega$ is a bounded domain of a complete Riemannian…

In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…

We extend the classical theory of variational interpolating splines to the case of compact Riemannian manifolds. Our consideration includes in particular such problems as interpolation of a function by its values on a discrete set of points…

We consider a class of parabolic variational inequalities with time dependent obstacle of the form $|{\boldsymbol u}(x,t)| \le p(x,t)$, where ${\boldsymbol u}$ is the velocity field of a fluid governed by the Navier--Stokes variational…

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…

In this paper, we consider optimization problems over closed embedded submanifolds of $\mathbb{R}^n$, which are defined by the constraints $c(x) = 0$. We propose a class of constraint dissolving approaches for these Riemannian optimization…

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

We are concerned with nonexistence results of nonnegative weak solutions for a class of quasilinear parabolic problems with a potential on complete noncompact Riemannian manifolds. In particular, we highlight the interplay between the…