43 citations · 239 across the 66 of their papers we have counts for
15 papers · 1 filter
Some iterative algorithms on Riemannian manifolds and Banach spaces with good global convergence guarantee
Tuyen Trung Truong
In this paper, we introduce some new iterative optimisation algorithms on Riemannian manifolds and Hilbert spaces which have good global convergence guarantees to local minima. Mor…
Backtracking New Q-Newton's method, Newton's flow, Voronoi's diagram and Stochastic root finding
John Erik Fornaess, Mi Hu, Tuyen Trung Truong +1
A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental perform…
Creating walls to avoid unwanted points in root finding and optimization
Tuyen Trung Truong
In root finding and optimization, there are many cases where there is a closed set one likes that the sequence constructed by one's favourite method will not converge to A (her…
Backtracking New Q-Newton's method: a good algorithm for optimization and solving systems of equations
Tuyen Trung Truong
In this paper, by combining the algorithm New Q-Newton's method - developed in previous joint work of the author - with Armijo's Backtracking line search, we resolve convergence is…
Generalisations and improvements of New Q-Newton's method Backtracking
Tuyen Trung Truong
In this paper, we propose a general framework for the algorithm New Q-Newton's method Backtracking, developed in the author's previous work. For a symmetric, square real matrix …
New Q-Newton's method meets Backtracking line search: good convergence guarantee, saddle points avoidance, quadratic rate of convergence, and easy implementation
Tuyen Trung Truong
In a recent joint work, the author has developed a modification of Newton's method, named New Q-Newton's method, which can avoid saddle points and has quadratic rate of convergence…
Unconstrained optimisation on Riemannian manifolds
Tuyen Trung Truong
In this paper, we give explicit descriptions of versions of (Local-) Backtracking Gradient Descent and New Q-Newton's method to the Riemannian setting.Here are some easy to state c…
Asymptotic behaviour of learning rates in Armijo's condition
Tuyen Trung Truong, Tuan Hang Nguyen
Fix a constant . For a function , a point and a positive number , we say that Armijo's condition is satisfied if $f(x-δ\…
A fast and simple modification of Newton's method helping to avoid saddle points
Tuyen Trung Truong, Tat Dat To, Tuan Hang Nguyen +3
We propose in this paper New Q-Newton's method. The update rule is very simple conceptually, for example where , with $A_n=\n…
Coordinate-wise Armijo's condition: General case
Tuyen Trung Truong
Let be coordinates for the product space . Let be a funct…
Some convergent results for Backtracking Gradient Descent method on Banach spaces
Tuyen Trung Truong
Our main result concerns the following condition: {\bf Condition C.} Let be a Banach space. A function satisfies Condition C if whenever $\{x_…
Backtracking Gradient Descent allowing unbounded learning rates
Tuyen Trung Truong
In unconstrained optimisation on an Euclidean space, to prove convergence in Gradient Descent processes (GD) it usually is required that the learnin…
Coordinate-wise Armijo's condition
Tuyen Trung Truong
Let be coordinates for the product space . Let be a funct…
Convergence to minima for the continuous version of Backtracking Gradient Descent
Tuyen Trung Truong
The main result of this paper is: {\bf Theorem.} Let be a function, so that is locally Lipschitz continuous. Assume moreov…
Backtracking gradient descent method for general functions, with applications to Deep Learning
Tuyen Trung Truong, Tuan Hang Nguyen
While Standard gradient descent is one very popular optimisation method, its convergence cannot be proven beyond the class of functions whose gradient is globally Lipschitz continu…