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09/20/2023
Multiplying poles to avoid unwanted points in root finding and optimization
In root finding and optimization, there are many cases where there is a ...
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09/12/2022
Backtracking New Q-Newton's method: a good algorithm for optimization and solving systems of equations
In this paper, by combining the algorithm New Q-Newton's method - develo...
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08/30/2022
Some interesting birational morphisms of smooth affine quadric 3-folds
We study a family of birational maps of smooth affine quadric 3-folds x_...
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04/13/2022
CapillaryX: A Software Design Pattern for Analyzing Medical Images in Real-time using Deep Learning
Recent advances in digital imaging, e.g., increased number of pixels cap...
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10/14/2021
A more direct and better variant of New Q-Newton's method Backtracking for m equations in m variables
In this paper we apply the ideas of New Q-Newton's method directly to a ...
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09/23/2021
Generalisations and improvements of New Q-Newton's method Backtracking
In this paper, we propose a general framework for the algorithm New Q-Ne...
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08/23/2021
New Q-Newton's method meets Backtracking line search: good convergence guarantee, saddle points avoidance, quadratic rate of convergence, and easy implementation
In a recent joint work, the author has developed a modification of Newto...
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04/23/2021
CapillaryNet: An Automated System to Analyze Microcirculation Videos from Handheld Vital Microscopy
Capillaries are the smallest vessels in the body responsible for the del...
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08/25/2020
Unconstrained optimisation on Riemannian manifolds
In this paper, we give explicit descriptions of versions of (Local-) Bac...
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07/07/2020
Asymptotic behaviour of learning rates in Armijo's condition
Fix a constant 0<α <1. For a C^1 function f:ℝ^k→ℝ, a point x and a posit...
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06/02/2020
A modification of quasi-Newton's methods helping to avoid saddle points
We recall that if A is an invertible and symmetric real m× m matrix, the...
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03/11/2020
Coordinate-wise Armijo's condition: General case
Let z=(x,y) be coordinates for the product space R^m_1×R^m_2. Let f:R^m_...
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01/16/2020
Some convergent results for Backtracking Gradient Descent method on Banach spaces
Our main result concerns the following condition: Condition C. Let X ...
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01/07/2020
Backtracking Gradient Descent allowing unbounded learning rates
In unconstrained optimisation on an Euclidean space, to prove convergenc...
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11/18/2019
Coordinate-wise Armijo's condition
Let z=(x,y) be coordinates for the product space R^m_1×R^m_2. Let f:R^m_...
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11/11/2019
