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In this paper, we aim at unifying, simplifying and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce the notion of nice primal algorithmic map, which plays a central…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
The time dependent complex Schr\"odinger equation with cubic nonlinearity is solved by constructing differential quadrature algorithm based on sinc functions. Reduction to a coupled system of real equations enables to approach the space…
We improve the algorithm to noninvasively update the response matrix using information from the orbit-feedback system, described in [1]. The new version is capable of adapting to slow changes of the lattice, albeit at the expense of…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
Convergence acceleration of flow simulations to their steady states at lower Mach numbers can be achieved via preconditioning the lattice Boltzmann (LB) schemes that alleviate the associated numerical stiffness, which have so far been…
In this work, a nonlinear momentum method is introduced to enhance the convergence performance of momentum-based gradient optimization algorithms. Classical momentum methods, such as the Heavy Ball method, can be viewed as a dynamical…
This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite…
Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…
This paper presents a large-scale strip adjustment method for LiDAR mobile mapping data, yielding highly precise maps. It uses several concepts to achieve scalability. First, an efficient graph-based pre-segmentation is used, which directly…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
Level-sensitive latches are widely used in high- performance designs. For such circuits efficient statistical timing analysis algorithms are needed to take increasing process vari- ations into account. But existing methods solving this…
We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace--Beltrami…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
It is well known that adding any skew symmetric matrix to the gradient of Langevin dynamics algorithm results in a non-reversible diffusion with improved convergence rate. This paper presents a gradient algorithm to adaptively optimize the…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…
An efficient nonlinear contrast source inversion scheme for electromagnetic imaging of sparse two-dimensional investigation domains is proposed. To avoid generating a sequence of linear sparse optimization problems, the non-linearity is…
Decentralized optimization is effective to save communication in large-scale machine learning. Although numerous algorithms have been proposed with theoretical guarantees and empirical successes, the performance limits in decentralized…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…