Related papers: On projection mappings and the gradient projection…
In this paper, we propose a new inexact version of the projected subgradient method to solve nondifferentiable constrained convex optimization problems. The method combine $\epsilon$-subgradient method with a procedure to obtain a feasible…
We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f({\kappa}) = {\sigma} over (0,1) with a prescribed asymptotic boundary {\Gamma} at infinity…
We show that for a very general class of curvature functions defined in the positive cone, the problem of finding a complete strictly locally convex hypersurface in $H^n+1$ satisfying $f(\kappa)=\sigma\in(0, 1)$ with a prescribed asymptotic…
This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed in the literature and characterised by the inclusion of non-local operators that give power law damping as…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…
The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…
In this paper we introduce a new geometric flow --- the hyperbolic gradient flow for graphs in the $(n+1)$-dimensional Euclidean space $\mathbb{R}^{n+1}$. This kind of flow is new and very natural to understand the geometry of manifolds. We…
This work focuses on convergence analysis of the projected gradient method for solving constrained convex minimization problem in Hilbert spaces. We show that the sequence of points generated by the method employing the Armijo linesearch…
The WKB approximation of geometrical optics is widely used in plasma physics, quantum mechanics and reduced wave modeling in general. However, it is well-known that the approximation breaks down at focal and turning points. In this work we…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
We further research on the accelerated optimization phenomenon on Riemannian manifolds by introducing accelerated global first-order methods for the optimization of $L$-smooth and geodesically convex (g-convex) or $\mu$-strongly g-convex…
We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic…
Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
We develop a short-step interior point method to optimize a linear function over a convex body assuming that one only knows a membership oracle for this body. The approach is based on Abernethy and Hazan's sketch of a universal interior…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
In this paper, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski-type…
Modeling the inherent hierarchical structure of 3D objects and 3D scenes is highly desirable, as it enables a more holistic understanding of environments for autonomous agents. Accomplishing this with implicit representations, such as…
The aim of this paper is to deepen the convergence analysis of the scaled gradient projection (SGP) method, proposed by Bonettini et al. in a recent paper for constrained smooth optimization. The main feature of SGP is the presence of a…