Related papers: Adaptative Step Size Selection for Homotopy Method…
In this paper, we study numerical approximations for stochastic differential equations (SDEs) that use adaptive step sizes. In particular, we consider a general setting where decisions to reduce step sizes are allowed to depend on the…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
We numerically investigate the performance of the short path optimization algorithm on a toy problem, with the potential chosen to depend only on the total Hamming weight to allow simulation of larger systems. We consider classes of…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
Globalization concepts for Newton-type iteration schemes are widely used when solving nonlinear problems numerically. Most of these schemes are based on a predictor/corrector step size methodology with the aim of steering an initial guess…
An algorithm is presented for momentum gradient descent optimization based on the first-order differential equation of the Newtonian dynamics. The fictitious mass is introduced to the dynamics of momentum for regularizing the adaptive…
We improve the understanding of the $\textit{golden ratio algorithm}$, which solves monotone variational inequalities (VI) and convex-concave min-max problems via the distinctive feature of adapting the step sizes to the local Lipschitz…
We consider the use of a curvature-adaptive step size in gradient-based iterative methods, including quasi-Newton methods, for minimizing self-concordant functions, extending an approach first proposed for Newton's method by Nesterov. This…
We consider the extension of the method of Gauss-Newton from complex floating-point arithmetic to the field of truncated power series with complex floating-point coefficients. With linearization we formulate a linear system where the…
We study the use of inverse harmonic Rayleigh quotients with target for the stepsize selection in gradient methods for nonlinear unconstrained optimization problems. This provides not only an elegant and flexible framework to parametrize…
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction…
The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…
Existing methods for nonconvex bilevel optimization (NBO) require prior knowledge of first- and second-order problem-specific parameters (e.g., Lipschitz constants and the Polyak-{\L}ojasiewicz (P{\L}) parameters) to set step sizes, a…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
In this paper has been considered probability-one global convergence of NFPH (Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations and has been proposed a probability-one homotopy algorithm to solve a regularized…
A scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed. This scheme leads to the same limiting differential equation as the original scheme and therefore has the same…
A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are…
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…
Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input…