相关论文: Eighth-order Derivative-Free Family of Iterative M…

Using the Thue-Siegel method, we obtain effective improvements on Liouville's irrationality measure for certain one-parameter families of algebraic numbers, defined by equations of the type $(t-a)Q(t)+P(t)=0$. We apply these to some…

In this article we combine the projective Landweber method, recently proposed by the authors, with Kaczmarz's method for solving systems of non-linear ill-posed equations. The underlying assumption used in this work is the tangential cone…

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward…

We develop an algorithm for minimizing a function using $n$ batched function value measurements at each of $T$ rounds by using classifiers to identify a function's sublevel set. We show that sufficiently accurate classifiers can achieve…

The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…

We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…

The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…

In the paper [Muhammad Aslam Noor, Khalida Inayat Noor, Three-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 183 (2006), pp. 322-327 ], Authors presented an algorithm (\textbf{Algorithm 2.3}) and stated…

We leverage the connections between nonexpansive maps, monotone Lipschitz operators, and proximal mappings to obtain near-optimal (i.e., optimal up to poly-log factors in terms of iteration complexity) and parameter-free methods for solving…

In this paper we analyse the pathwise approximation of stochastic differential equations by polynomial splines with free knots. The pathwise distance between the solution and its approximation is measured globally on the unit interval in…

Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…

We establish the existence theory of several commonly used finite element (FE) nonlinear fully discrete solutions, and the convergence theory of a linearized iteration. First, it is shown for standard FE, SUPG and edge-averaged method…

Starting from an A-stable rational approximation to $\rm{e}^z$ of order $p$, $$r(z)= 1+ z+ \cdots + z^p/ p! + O(z^{p+1}),$$ families of stable methods are proposed to time discretize abstract IVP's of the type $u'(t) = A u(t) + f(t)$. These…

Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…

This work introduces the nested-set Hessian approximation, a second-order approximation method that can be used in any derivative-free optimization routine that requires such information. It is built on the foundation of the generalized…

We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…

There are thousands of papers on rootfinding for nonlinear scalar equations. Here is one more, to talk about an apparently new method, which I call ``Inverse Cubic Iteration'' (ICI) in analogy to the Inverse Quadratic Iteration in Richard…

In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…