Global Optimization Algorithms Based On α-dense Curves

In recent years, many scholars have been devoted to the global optimization prob-lem algorithm, and have made certain progress. The thesis mainly studies the global optimization problem algorithms based on α-dense curves. In the first phase of the algorithm, α-dense curves allow us to convert the multivariate global optimization problems to univariate ones; in the second phase, by combining the constructed filled function or integral function, the algorithm aims to find a better minimizer of the prob-lem. Repeating the above process until the time when we can finally find the global minimizer. The algorithms seek to deep development and are of global convergence. This thesis mainly consists of four chapters:Chapter 1, the basic definition and theorem of global optimization are given, we also introduce several local optimization algorithms and simple deterministic algorithms for solving global optimization problems, providing guidance for further study and promotion.Chapter 2, we give the definition and related properties of α-dense curve, enu-merate several kinds of α-dense curves.Chapter 3, a new definition of filled function has been proposed and we construct a new filled function and algorithm according to the definition, later in this chapter we use α-dense curves to convert the multivariate global optimization problem into a univariate one, constructing another new algorithm. Finally, the results of numerical experiments verify the efficiency of the algorithms.Chapter 4, we study an integral function algorithm based on α-dense curve and design the corresponding algorithm, at last, we analyze the convergence of the algorithm. Numerical results show the validity and reliability of the algorithm.