Related papers: A non-monotone smoothing Newton algorithm for solv…
Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a…
A Newton-type active set algorithm for large-scale minimization subject to polyhedral constraints is proposed. The algorithm consists of a gradient projection step, a second-order Newton-type step in the null space of the constraint matrix,…
Inspired by the decomposition in the hybrid quantum-classical optimization algorithm we introduced in arXiv:1902.04215, we propose here a new (fully classical) approach to solving certain non-convex integer programs using Graver bases. This…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
This paper considers the generalized continuation Newton method and thetrust-region updating strategy for the underdetermined system of nonlinear equations. Moreover, in order to improve its computational efficiency, the new method will not…
As second-order methods, Gauss--Newton-type methods can be more effective than first-order methods for the solution of nonsmooth optimization problems with expensive-to-evaluate smooth components. Such methods, however, often do not…
We build upon Estrin et al. (2019) to develop a general constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970, 1973b). Although Fletcher's approach has historically been considered…
In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…
We introduce a notion of self-concordant smoothing for minimizing the sum of two convex functions, one of which is smooth and the other nonsmooth. The key highlight is a natural property of the resulting problem's structure that yields a…
One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focus on developing…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such perturbations. To develop a more robust quasi-Newton method, we…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
The global minimum point of an optimization problem is of interest in engineering fields and it is difficult to be found, especially for a nonconvex large-scale optimization problem. In this article, we consider a new memetic algorithm for…
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…
Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…
In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general…