This monograph covers some recent advances in a range of acceleration techniques frequently used convex optimization. We first use quadratic optimization problems to introduce two key families methods, namely momentum and nested schemes. They coincide the case form Chebyshev method. discuss methods detail, starting with seminal work Nesterov structure convergence proofs using few master templat...

We propose a new algorithm for minimizing regularized empirical loss: Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each iteration we update a random subset of the dual variables. However, unlike existing methods such as stochastic dual coordinate ascent, SDNA is capable of utilizing all local curvature information contained in the examples, which leads to striking impr...

We consider the optical flow estimation problem with lp sub-quadratic regularization, where 0 ≤ p ≤ 1. As in other image analysis tasks based on functional minimization, sub-quadratic regularization is expected to admit discontinuities and avoid oversmoothing of the estimated optical flow field. The problem is mathematically challenging, since the regularization term is non-differentiable. It i...

This paper studies the problem of robust stabilization for linear uncertain systems via logarithmic quantized feedback. Our work is based on a new method for the analysis of quantized feedback. More specifically, we characterize the quantization error using a simple sector bound. It is shown in our previous work that this method yields the same result on the coarsest quantization density as in ...

Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and analyze a class of fast and stable sequential optimization methods for computing maximum likelihood estimates and study its convergence properties. These methods...

For any number field, J.-F. Jaulent introduced a new invariant called the group of logarithmic classes in 1994. This invariant is proved to be closely related to the wild kernels of number fields. In this paper, we show how to compute the kernel of the natural homomorphism from the group of logarithmic classes to the group of p-ideal classes by computing the p-adic regulator which is a classica...

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often large scale. With aim, devise an infeasible interior point method, blended with proximal method multipliers, which in turn results a primal-dual regularized method. Application gives rise to sequence increasingly ill-conditioned systems cannot always be solved by factorization methods,...

Abstract The final value problem for the Brinkman–Forchheimer–Kelvin–Voigt equations is analysed quadratic and cubic types of Forchheimer nonlinearity. main term in allowed to be fully anisotropic. It shown that solution depends continuously on data provided satisfies an a priori bound $$L^3.$$ L <m...

The MM principle is a device for creating optimization algorithms satisfying the ascent or descent property. The current survey emphasizes the role of the MM principle in nonlinear programming. For smooth functions, one can construct an adaptive interior point method based on scaled Bregman barriers. This algorithm does not follow the central path. For convex programming subject to nonsmooth co...

in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...