相关论文: Stabilized Barzilai-Borwein method
We propose a new \textit{randomized Bregman (block) coordinate descent} (RBCD) method for minimizing a composite problem, where the objective function could be either convex or nonconvex, and the smooth part are freed from the global…
We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…
Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
Adam is a popular variant of stochastic gradient descent for finding a local minimizer of a function. In the constant stepsize regime, assuming that the objective function is differentiable and non-convex, we establish the convergence in…
We study a second order BDF (Backward Differentiation Formula) scheme for the numerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations. The scheme under consideration is implicit, non-monotone, and second order accurate…
Consensus-based optimization (CBO) is a powerful and versatile zero-order multi-particle method designed to provably solve high-dimensional global optimization problems, including those that are genuinely nonconvex or nonsmooth. The method…
We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…
It is well known that the seven-step backward difference formula (BDF) is unstable for the parabolic equations, since it is not even zero-stable. However, a linear combination of two non zero-stable schemes, namely the seven-step BDF and…
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…
This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…
This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…
Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of…
This manuscript presents the following: (1) an improved version of the Binary Simultaneous Perturbation Stochastic Approximation (SPSA) Method for feature selection in machine learning (Aksakalli and Malekipirbazari, Pattern Recognition…
Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three…
Gradient methods are among the simplest yet most widely used algorithms for unconstrained optimization. Motivated by a geometric property of the steepest descent (SD) method that can alleviate the zigzag behavior in quadratic problems, we…
We consider the pricing and the sensitivity calculation of continuously monitored barrier options. Standard Monte Carlo algorithms work well for pricing these options. Therefore they do not behave stable with respect to numerical…