RETRACTED: Canonical duality–triality theory: bridge between nonconvex analysis/mechanics and global optimization in complex systems

2015 ◽  
Vol 21 (3) ◽  
pp. NP3-NP4 ◽  
Author(s):  
David Yang Gao ◽  
Ning Ruan ◽  
Vittorio Latorre
Keyword(s):  
Global Optimization ◽  
Complex Systems ◽  
Canonical Duality ◽  
Triality Theory ◽  
Nonconvex Analysis

Multicanonical basin hopping: A new global optimization method for complex systems

2004 ◽  
Vol 120 (12) ◽  
pp. 5536-5542 ◽  
Author(s):  
Lixin Zhan ◽  
Bart Piwowar ◽  
Wing-Ki Liu ◽  
P. J. Hsu ◽  
S. K. Lai ◽  
...  
Keyword(s):  
Global Optimization ◽  
Complex Systems ◽  
Optimization Method ◽  
Global Optimization Method ◽  
Basin Hopping

scholarly journals Complete Solutions to General Box-Constrained Global Optimization Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Dan Wu ◽  
Youlin Shang
Keyword(s):  
Optimal Control ◽  
Global Optimization ◽  
Optimization Problems ◽  
Analytical Form ◽  
Optimization Method ◽  
Global Optimality ◽  
Constrained Optimal Control ◽  
Canonical Duality ◽  
General Nonlinear Programming ◽  
Complete Solutions

This paper presents a global optimization method for solving general nonlinear programming problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained, and criteria for global optimality and existence of solutions are given. Our theorems improve and generalize recent known results in the canonical duality theory. Applications to a class of constrained optimal control problems are discussed. Particularly, an analytical form of the optimal control is expressed. Some examples are included to illustrate this new approach.

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