arXiv research

Proposes a nonconvex optimization method for sparse logistic regression.

Unified approach tackles high-dimensional tensor bandits with convex optimization and weakly decomposable regularizers.

New algorithm solves complex non-convex problems efficiently.

Convex surfaces derived from specific Riemannian manifolds with high regularity.

Paper extends SMM to weakly convex and multi-convex surrogates for non-convex optimization.

New method uses deep learning to solve inverse problems with provable guarantees.

New convergence rates found for PnP methods using MMSE denoisers.

Weakly convex polyhedra which are star-shaped with respect to one of their vertices are infinitesimally rigid. This is a partial answer to the question whether every decomposable weakly convex polyhedron is infinitesimally rigid. The proof uses a recent result of Izmestiev on the geometry of convex caps.

We show that closed hypersurfaces in Euclidean space with nonnegative scalar curvature are weakly mean convex. In contrast, the statement is no longer true if the scalar curvature is replaced by the k-th mean curvature, for k greater than 2, as we construct the counter-examples for all k greater than 2. Our proof relie…

Proximal methods avoid local minima in weakly convex problems.

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In…

Smooth analog of Gromov's dihedral rigidity for 3D weakly convex domains.

Improved bounds for MALA in non-convex sampling problems.

Paper develops algorithms for solving non-convex non-concave problems with applications in GAN training.

We show the regularity of, and derive a-priori estimates for (weakly) harmonic maps from a Riemannian manifold into a Euclidean sphere under the assumption that the image avoids some neighborhood of a half-equator. The proofs combine constructions of strictly convex functions and the regularity theory of quasi-linear e…

Paper proposes DC functions for better regularization of inverse problems with theoretical guarantees.

Expanding FCCO to non-smooth weakly-convex problems, improving deep learning performance.

Neural network approximates weakly efficient frontier of convex vector optimization problems.

Adaptive algorithm AMSGrad converges for weakly convex constrained optimization problems.

On R^n endowed with a riemannian metric of bounded nonpositive curvature, the weakly convex closed subsets are topologically trivial. The stability of such subsets under intersection characterizes the euclidean spaces.

This paper improves inverse problem solving with weakly convex regularisers and proves convergence.

SGD avoids critical points on weakly convex functions.

This paper proves energy convexity for bi-harmonic maps into spheres, with applications to heat flow and uniqueness.

A connected combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. A connected combinatorial 2-manifold is called weakly regular if it has a vertex-transitive automorphism group. Clearly, a weakly regular combinatorial 2-manifold is degree-regular and a degree-regular combinator…

The paper proves smoothness of weakly biharmonic almost complex structures in dimension four.

The study shows how to regularize weakly harmonic maps using Sobolev norms and Coulomb frames.

New adaptive methods solve weakly convex stochastic optimization problems.

Paper tackles efficient learning of non-convex hypotheses in metric spaces.

Paper analyzes convergence of stochastic methods under heavy-tailed noise.

The paper proves a Schwarz lemma for weakly Kähler-Finsler manifolds.

Study on polyhedra rigidity, finding non-existence of flexible weakly convex decomposable polyhedra.

New single-loop algorithm tackles weakly convex constraints in stochastic optimization.

Solves weakly supervised regression using low-rank approximations and manifold regularization.

The study compares spectral volumes of manifolds with weakly convex boundaries.

ProxSPS improves on SPS for regularization tasks, offering better stability and performance.

Decentralized method solves saddle point problems with theoretical guarantees.

A submanifold $M^m$ of a Euclidean space $R^{m+p}$ is said to have harmonic mean curvature vector field if $Δ\vec{H}=0$, where $\vec{H}$ is the mean curvature vector field of $M\hookrightarrow R^{m+p}$ and $Δ$ is the rough Laplacian on $M$. There is a conjecture named after Bangyen Chen which states that submanifolds o…

Streaming method improves weakly submodular function approximation.

We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the free boundary for weakly Dirac-harmonic maps from spin Riemann surfaces. Our met…

Study on special convex sets in n-dimensional space.

Study LASSO for high-dimensional VAR models with weakly dependent innovations.

Develops a new SPP algorithm with variance reduction for weakly convex optimization.

Gradient descent performs well on weakly convex losses, offering generalization guarantees.

In this paper we consider three-manifolds with weakly umbilic boundary (the Second Fundamental form of the boundary is a constant multiple of the metric). We show that if the initial manifold has positive Ricci curvature and the boundary is convex (nonnegative Second Fundamental form), its metric can be deformed via th…

Unified definition of mass aspect function for weakly regular hyperbolic manifolds.

On some specified convex supporting sets of spheres, we find a generalized longitude function whose level sets are totally geodesic. Given an arbitrary (weakly) harmonic map into spheres, the composition of the generalized longitude function and harmonic map satisfies an elliptic equation of divergence type. With the a…

New class of complex manifolds defined, properties studied.

In this paper we describe the notion of a weak lipschitzianity of a mapping on a $C^{q}$ stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the …