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Application of the Nelder–Mead Method to Optimize the Way for Selection of the Likhachev–Volkov Model Constants
AbstractA new way was proposed to select the constants for the modified Likhachev–Volkov microstructural model to describe the reversible strain...
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Practical initialization of the Nelder–Mead method for computationally expensive optimization problems
Black-box optimization (BBO) algorithms are widely employed by practitioners to address computationally expensive real-world problems such as...
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Improvement of the Nelder-Mead method using Direct Inversion in Iterative Subspace
The Nelder-Mead (NM) method is a popular derivative-free optimization algorithm owing to its fast convergence and robustness. However, it is known...
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Optimal Parameter Estimation Techniques for Complex Nonlinear Systems
Accurate parameter estimation and state identification within nonlinear systems are fundamental challenges addressed by optimization techniques. This...
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Detecting self-organising patterns in crowd motion: effect of optimisation algorithms
The escalating process of urbanization has raised concerns about incidents arising from overcrowding, necessitating a deep understanding of large...
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A New Regularly Varying Discrete Distribution Generated by Waring-Type Probability
AbstractIn this paper, based on the discretization method, we construct a new 2-parameter regularly varying discrete distribution generated by...
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Inverse Problem of Pure Bending of a Beam under Creep Conditions
AbstractWe propose an algorithm for solving the inverse problem of forming structural members under creep conditions using the Nelder–Mead...
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Determination of a Preliminary Orbit by the Cauchy–Kuryshev–Perov Geometric Method
AbstractThe determination of preliminary orbits of celestial bodies is of interest to observational astronomy in terms of discovering new bodies or...
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A Gradient-Free Method for Multi-objective Optimization Problem
In this chapter, a gradient-free method is proposed for solving the multi-objective optimization problem in higher dimension. The concept is...
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A Nonconvex Nonsmooth Image Prior Based on the Hyperbolic Tangent Function
In this paper, we propose a nonconvex and nonsmooth image prior based on the hyperbolic tangent function and apply it as a regularization term for...
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Direct Methods for Constrained Optimization
As we have already seen in Chap. 9 , the direct methods for unconstrained optimization do not use...
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Discovery and Interactive Representation of the Dimensionless Parameter-Space of the Spring-Loaded Inverted Pendulum Model of Legged Locomotion Using Surface Interpolation
The spring-loaded inverted pendulum is a widely used model of legged locomotion. However, a complete map of the dimensionless parameter regions that...
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Numerical Solution of Two-Point Static Problems for Distributed Extended Systems by Means of the Nelder–Mead Method
The authors describe a numerical algorithm for reducing two-point static problems of distributed extended systems in the field of body and surface...
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A Randomised Non-descent Method for Global Optimisation
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of...
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Modeling and simulation studies for some truncated discrete distributions generated by stable densities
Some discrete distributions generated by stable densities (DGSDs) could be considered as models for describing phenomena arising in bioinformatics....
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Proper initialization is crucial for the Nelder–Mead simplex search
The Nelder–Mead simplex search as one of the oldest direct search methods is still in use today. Despite its flaws, such as possible convergence to...
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Numerical Methods of Optimization
The numerical methods of optimization start with optimizing functions of one variable, bisection, Fibonacci, and Newton. Then, functions of several...
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Numerical Solution of the Inverse Problem for Diffusion-Logistic Model Arising in Online Social Networks
The information propagation in online social networks is characterized by a nonlinear partial differential equation with the Neumann boundary...
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The Nelder–Mead simplex algorithm with perturbed centroid for high-dimensional function optimization
It is a well known fact that the widely used Nelder–Mead (NM) optimization method soon becomes inefficient as the dimension of the problem grows. It...
