An integral function and vector sequence method for unconstrained global optimization

An integral function and a vector sequence are constructed in this paper. Their theoretical and numerical properties are investigated. Based on the integral function and the vector sequence, an algorithm is proposed for solving a class of unconstrained global optimization problems. For the algorithm, convergence to a global minimizer is discussed under some conditions. Some typical examples are tested to illustrate the efficiency of the algorithm.

[1]  Reiner Horst,et al.  Introduction to Global Optimization (Nonconvex Optimization and Its Applications) , 2002 .

[2]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[3]  Qiaoming Han,et al.  Revised filled function methods for global optimization , 2001, Appl. Math. Comput..

[4]  Panos M. Pardalos,et al.  Constrained Global Optimization: Algorithms and Applications , 1987, Lecture Notes in Computer Science.

[5]  Marco Locatelli,et al.  A Note on the Griewank Test Function , 2003, J. Glob. Optim..

[6]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .

[7]  C. Floudas.  Handbook of Test Problems in Local and Global Optimization , 1999 .

[8]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms, 3/E. , 2019 .

[9]  Bedri C. Cetin,et al.  Terminal repeller unconstrained subenergy tunneling (trust) for fast global optimization , 1993 .

[10]  Stefano Lucidi,et al.  New Classes of Globally Convexized Filled Functions for Global Optimization , 2002, J. Glob. Optim..

[11]  Renpu Ge,et al.  A Filled Function Method for Finding a Global Minimizer of a Function of Several Variables , 1990, Math. Program..

[12]  A. V. Levy,et al.  The Tunneling Algorithm for the Global Minimization of Functions , 1985 .

[13]  Yong Yao,et al.  Dynamic tunneling algorithm for global optimization , 1989, IEEE Trans. Syst. Man Cybern..

[14]  Panos M. Pardalos,et al.  Introduction to Global Optimization , 2000, Introduction to Global Optimization.

[15]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[16]  R. Ge,et al.  The globally convexized filled functions for global optimization , 1990 .