Related papers: On Topology Optimization and Canonical Duality Met…
A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved…
This paper demonstrates a mathematically correct and computationally powerful method for solving 3D topology optimization problems. This method is based on canonical duality theory (CDT) developed by Gao in nonconvex mechanics and global…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…
Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems…
This paper presents a new canonical duality methodology for solving general nonlinear dynamical systems. Instead of the conventional iterative methods, the discretized nonlinear system is first formulated as a global optimization problem…
DY Gao together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of constrained optimization problems. Unfortunately, in several papers on this subject there are unclear statements, not…
Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide class of challenging problems from real-world applications.…
DY Gao solely or together with some of his collaborators applied his Canonical duality theory (CDT) for solving some quadratic optimization problems with quadratic constraints. Unfortunately, in almost all papers we read on CDT there are…
This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and…
This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows that by using the canonical duality…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…
The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived.…
In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…
This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little…
General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can…
This paper presents an efficient 51 lines Matlab code to solve topology optimization problems. By the fact that the presented code is based on an hard 0-1 optimization method that handles the integer part of the optimization in a simple…
Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology…