A global minimization algorithm for a class of one-dimensional functions
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TLDR
In this article, an algorithm was developed for finding the global minimum of a continuously differentiable function on a compact interval in R 1, where the function is assumed to be the sum of a convex and a concave function, each of which belongs to C 1 [a, b ].About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1978-02-01 and is currently open access. It has received 9 citations till now. The article focuses on the topics: Convex function & Concave function.read more
Citations
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Cord-slope form of Taylor's expansion in univariate global optimization
TL;DR: In this paper, Taylor's formula is used to bound the slope of the cord of a univariate function at a given point, which leads in turn to bounding the values of the function itself.
Global Minimization of Univariate Functions by Sequential Polynomial Approximation
TL;DR: A new ordered sequential algorithm in which step-sizes are such that the function can be approximated locally by a polynomial with a precision of e.g. cm2, which explores efficiently the vicinity of the optimum, while other sequential algorithms do not.
Journal ArticleDOI
Global minimization of univariate functions by sequential polynomial approximation
TL;DR: In this paper, an ordered sequential algorithm for the global minimization of univariate functions over an interval is proposed, in which step-sizes are such that the function can be approximated locally by a polynomial with a precision of e.g.
Journal Article
Low Regret Binary Sampling Method for Efficient Global Optimization of Univariate Functions
TL;DR: This work proposes a computationally efficient algorithm for the problem of global optimization in univariate loss functions and analytically extends its results for a broader class of functions that covers more complex regularity conditions.
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Modified Piyavskii's Global One-Dimensional Optimization of a Differentiable Function
TL;DR: In this article, a modified Piyavskii's algorithm (nC) was proposed to maximize a univariate differentiable function by iteratively constructing an upper bound of a piece-wise concave function of f and evaluating f at a point where Φ reaches its maximum.
References
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Book
Algorithms for Minimization Without Derivatives
TL;DR: In this paper, a monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions, and some of these methods can be used to find approximate minima as well.
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A Sequential Method Seeking the Global Maximum of a Function
TL;DR: In this article, a sequential search method for finding the global maximum of an objective function is proposed, which is applicable to a single variable defined on a closed interval and such that some bound on its rate of change is available.
Journal ArticleDOI
Introduction to Optimization Techniques: Fundamentals and Applications of Nonlinear Programming
TL;DR: In this paper, the authors introduce the basic techniques for locating extrema (minima or maxima) of a function of several variables, and present a standard set of techniques for unconstrained function extremization.
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