Quasi-Newton methods based on ordinary differential equation approach for unconstrained nonlinear optimization

2014 ◽  
Vol 233 ◽  
pp. 272-291 ◽  
Author(s):  
Farzin Modarres Khiyabani ◽  
Wah June Leong
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlinear Optimization ◽  
Equation Approach ◽  
Newton Methods ◽  
Unconstrained Nonlinear Optimization ◽  
Quasi Newton

scholarly journals From time series analysis to a modified ordinary differential equation

2018 ◽  
Vol 12 (2) ◽  
pp. 85-90
Author(s):  
Meiyu Xue ◽  
Choi-Hong Lai
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Time Series ◽  
Time Series Analysis ◽  
Stock Prices ◽  
Time Frame ◽  
Equation Approach ◽  
Advantages And Disadvantages ◽  
Series Analysis ◽  
Bank Stock

In understanding Big Data, people are interested to obtain the trend and dynamics of a given set of temporal data, which in turn can be used to predict possible futures. This paper examines a time series analysis method and an ordinary differential equation approach in modeling the price movements of petroleum price and of three different bank stock prices over a time frame of three years. Computational tests consist of a range of data fitting models in order to understand the advantages and disadvantages of these two approaches. A modified ordinary differential equation model, with different forms of polynomials and periodic functions, is proposed. Numerical tests demonstrated the advantage of the modified ordinary differential equation approach. Computational properties of the modified ordinary differential equation are studied.

scholarly journals Rates of superlinear convergence for classical quasi-Newton methods

2021 ◽  
Author(s):  
Anton Rodomanov ◽  
Yurii Nesterov
Keyword(s):  
Nonlinear Optimization ◽  
Superlinear Convergence ◽  
Local Convergence ◽  
Lipschitz Constant ◽  
Rates Of Convergence ◽  
Newton Methods ◽  
Long Time ◽  
Broyden Class ◽  
Quasi Newton ◽  
Convexity Parameter

AbstractWe study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that asymptotically these methods converge superlinearly, the corresponding rates of convergence still remain unknown. In this paper, we address this problem. We obtain first explicit non-asymptotic rates of superlinear convergence for the standard quasi-Newton methods, which are based on the updating formulas from the convex Broyden class. In particular, for the well-known DFP and BFGS methods, we obtain the rates of the form $$(\frac{n L^2}{\mu ^2 k})^{k/2}$$ ( n L 2 μ 2 k ) k / 2 and $$(\frac{n L}{\mu k})^{k/2}$$ ( nL μ k ) k / 2 respectively, where k is the iteration counter, n is the dimension of the problem, $$\mu $$ μ is the strong convexity parameter, and L is the Lipschitz constant of the gradient.

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