Daniela Lera

Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization

A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization is presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically distorted by polynomials in order to introduce local minima. To determine a class, the user defines the following parameters: (i) problem dimension, (ii) number of local minima, (iii) value of the global minimum, (iv) radius of the attraction region of the global minimizer, (v) distance from the global minimizer to the vertex of the quadratic function. Then, all other necessary parameters are generated randomly for all 100 functions of the class. Full information about each test function including locations and values of all local minima is supplied to the user. Partial derivatives are also generated where possible.

Introduction to Global Optimization Exploiting Space-Filling Curves

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful .

Acceleration of Univariate Global Optimization Algorithms Working with Lipschitz Functions and Lipschitz First Derivatives

This paper deals with two kinds of the one-dimensional global optimization problem over a closed finite interval: (i) the objective function

An information global minimization algorithm using the local improvement technique

f(x)

Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants

satisfies the Lipschitz condition with a constant

Test Functions with Variable Attraction Regions for GlobalOptimization Problems

L

Global Minimization Algorithms for Holder Functions

; (ii) the first derivative of

Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization

f(x)

A local search method for continuous global optimization

satisfies the Lipschitz condition with a constant

A complexity analysis of local search algorithms in global optimization

M